Mountains and snow...

a) Zermatt, b) Zermatt. c) Zermatt, d) Zermatt, e) Oops! Ditto the Jungfraujoch. Either of these will have spectacular mountain scenery. Switzerland is at the high end of the price scale, at least 25% more than any place using the euro.
Perhaps Chamonix, at the base of the highest mountain in Europe. You can take the cable car (2 actually, since 1500 meters is a physical limit for vertical rise using a cable, they are back-to-back to lift you up 3000 meters) to Aiguille du Midi with great views of the surrounding glacier and peaks with minimal walking. If you stay a couple of days, you will have a good chance to do this in good weather, so you can pick the day when you are there. Lodging and food are not too dear in Chamonix.
Zermatt and Jungfrau have the option of using trains. Zermatt is a pricey town to stay in as far as lodging goes and cost of using the mountain railways. For the Jungfrau, staying in Interlaken is reasonable for Switzerland, but the cost of the rail trip to the Jungfraujoch will be in the 100 chf per person round trip. Again, stay a few days so you can pick an ideal time to go.

It's Kitzsteinhorn in Zell am See - Kaprun area in Austria. It's summer skiing on the glacier. You can get all the way there by public transportation. Google Kitzsteinhorn glacier.

Reading through your itinerary, the Swiss and French Alps are bit out of your way. Therefore I will suggest Hintertux, which is a year round glacier resort in Austria which is directly between Bavaria and Italy. They are on the euro, and not really on the top of the most well known tourist destinations, so the prices should be reasonable. Its is on your way near Innsbruck.
http://www.hintertuxergletscher.at/en/experience/natures-ice-palace.html

You will be there the least snowy time of year, so the mountains won't have their best snow-covered peaks look. The weather should be good but always be ready for any weather when you're in the mountains. Also, it's not unusual to have cloudy days where you won't even know you are surrounded by snow-covered peaks. You should check the weather forecast before you make a day trip of it.

There are plenty of options with trams that will get you up into the mountains without any more strenuous climbing than a flight of stairs. I'm surprised no one mentioned Garmisch, Berchtesgaden or other German Alp towns? They seem like the most convenient options.

Brad,
I was thinking about Zugspitze, Germany's highest mountain. Easy and affordable access from Garmisch Partenkirchen. But I'm not sure if it has the snow at that time of year or if you can at least see snow-covered mountains from its peak. Do you know?

In my limited experience early September can be cloudy/rainy in the Alps. We canceled our Zugspitze plans due to the weather. Lower altitudes were better but still not sunny much of the time we were there.

There is no snow left on the top of the Zugspitze by late August; just the small glacier lower down.

Their best chance for snow-covered peaks and slopes they can see up close would be, as noted above, Zermatt, the Jungfrau area, or Chamonix (which is farther out of the way for them). Of those, the Jungfraujoch experience is probably the more reliable for snow, but the most expensive ( and very crowded). The Matterhorn has summer skiing on the high glacier, and a cablecar which reaches 3880 meters. There is rustic accommodation there in shared 8-person rooms for 60 CHF pp with breakfast. Or they could stay in a mountain inn lower down and ride the cablecar up. There is also a lodge with private rooms at the top of the Gornergrat train ride ( the Kulmhotel) but it is quite expensive.

See www.zermatt.ch for more information. Prices should drop somewhat at the end of August.

I have a picture taken from a mountain above Pfronten, Germany, on Aug 30, '09, looking towards the Zugspitze, and the mountains are all devoid of snow. A week earlier, I was in Innsbruck and there was also no snow on the mountains. Of course, each year can be different.

At that time of year, finding snow is going to be a bit difficult. Of course that varies a bit from year-to-year.

As previously mentioned, your best bet is probably Chamonix, the Jungfraujoch or Zermatt. However, there is one concern to mention. As your parents are "heart patients", you should be aware that both Aguille du Midi and the Jungfraujoch are at an elevation of about 3800 M / 12K ft. If your parents have any altitude issues, that could be a problem.

Visiting the Jungfraujoch doesn't involve any cable cars, as the entire route is covered by an electrified rail line, which travels inside the mountain for a portion of the way (quite a feat, considering construction was started ~1896 without any modern equipment). As with many things in Switzerland, that trip will be expensive. You could also consider the trip to the Schilthorn via cable car, but your chances of being close to snow are probably remote (according to the webcam, it's shrouded in fog at the moment).

According to THIS webcam there will be snow visible at the Jungfraujoch, but it too seems to be shrouded in fog. You can scroll back in time to see whichever time-of-day you want to look at.

In Germany, a fresh dusting of snow is possible in August and September, but not something you can reasonably expect to coincide with your visit. And it will quickly melt within a day or two. As noted, if you really want to see snow, your best option is to head further west to the Berner Oberland, the Pennine Alps or the Mont Blanc massief. Some snow usually remains at Hintertux further to the south.

Thank you, everybody, for the very helpful suggestions and advice !!!! Very best, and wish you all a great summer, Suresh

I've been to both Zermatt and up the Jungfraujoch. They're both lovely.

The train ride up the Jungfraujoch is spectacular and I'd highly recommend it. I was there in January though - I'm not sure if there's any snow there this time of year.

Zermatt has a glacier above it, so there's always snow if you go high enough. The cable car goes really high (about 4000 metres IIRC).

According to Wikipedia, the elevation of Chamonix is 3,400' / 1,000 m, not 12,000' as stated in another post above.

Since his tour finished in September, it is all academic now....

Thanks everybody... eventually got scared off the really high peaks due to my parents' heart condition. But we found some snow in the mountains around Innsbruck, and got the "snow-capped peaks" view on the Bernina express route (but in a regular train) from Chur to Tirano - that was a great train ride. I wish we had known/realized that the windows in the train cabins can be opened... for next time.

Best, Suresh

Thanks for the report, Suresh. The Bernina express route was an excellent choice. We did that a month later (early October), also by regional train, and it was truly spectacular.

"According to Wikipedia, the elevation of Chamonix is 3,400' / 1,000 m, not 12,000' as stated in another post above."

The Wikipedia page on Chamonix lists the elevation of Chamonix as "995–4,810 m (3,264–15,781 ft)". It also says, "The north side of the summit of Mont Blanc, and therefore the summit itself are part of the village of Chamonix.".

Sounds like the parents could be in the village at just over 3000' and still see snow on Mont Blanc.

I really loved Chamonix. I would check with their doctor to see about taking the trip up the Aguille du Midi to see Mont Blanc. Even going up half way is impressive. Another alternative would be to not got quite so high and take the train that goes up toward the Mer du Glace. Maybe someone knows what you can see without walking too far. There was a pub with an outdoor cafe right at the station. I was just so exhausted from my hike that I wasn't looking around at that point.

People with heart conditions should consult their physicians and use caution in going to altitudes above 7000 feet, especially if they plan to do something strenuous such as uphill walking.

In response to your original question, I would suggest one of the ski areas in Germany, either Garmisch-Partenkirchen or Oberstdorf. Both are fairly low (Garmisch-Partenkirchen is 707m, 2319 ft, above sea level, Oberstdorf is at 813m, 2666 ft), both are readily accessible by rail from Munich, and their are abundant, easitly accessible ski slopes.

There are some ski slopes within walking distance of the station at Garmisch-Partenkirchen. I'm not sure if you can ride the lift one time during ski season, but the Hausbergbahn is a gondola; the top of the lift is at only 1310m, 4297 ft. If you are going on to Italy, it's a short train ride to Innsbruck and Brenner Pass. The line goes though Seefeld, Austria, elevation about 3600 ft.

Oberstdorf is on the way to Switzerland, just off the rail line to Lindau, on the way to Bodensee. The entire Iller valley, from Immenstadt up to Oberstdorf is filled with ski lifts, some not so high. From Oberstdorf Bahnhof you can take the Walserbus up into the Austrian valley of Kleinwalsertal, which is also filled with ski lifts. The top of the valley is the little village of Baad at 1244m, 4080 ft. In Germany, just before the bus gets to Kleinwalsertal, is the Söllereckbahn, another gondola, that goes up to 1358m, 4454 ft. In my opinion, the scenery in the Oberstdorf area is more impressive than in Garmisch-Partenkirchen.

There are some lower lifts down the Iller valley towards Immenstadt, but I don't know how many of them are gondolas. I think they are mostly chair lifts and rope tows.