autumn or spring in the Bavarian Alps?

My take is Spring for the wildflowers. Not sure you will find the snow-capped mountains you are looking for in Bavaria in May. That said... Hiking in the Nationalpark Berchtesgaden can be pretty spectacular. Dive the Roßfeldpanoramastraße. The valleys to the south of Obertsdorf and Tegernsee, around Hochries, Garmisch and Mittenwald. Pretty much anywhere along the border with Austria. Some of the mountain Alm may not be open yet. That might help you decide where to hike if you want a lunch and a drink etc.

Thanks for the suggestion about wildflowers--that's a real bonus!

This massively depends on elevation. The Alps are far north. I live in Seattle, a bit farther south than the area you were talking about. Last year in June 4000 ft was still impassable in our local mountains. Depending on the snow pack in given year year, that can also be the case in Europe.

Regarding wildflowers, they also depend on elevation. Prime wildflower season in lake Tahoe area is early July.

So if you know your routes, you have good information to base your choices on. Keep in mind that where you sleep can be lower than if you need/want to hike higher, which is the usual pattern in the mountains.

Also note that you can walk across snow. It's just physically harder and can be more dangerous. Poles and shoe traction devices, if necessary, go a long way to making hiking over steeper snow manageable, but they don't alleviate all the risk.

Given that you are day hiking, in May you can always choose lower elevation hikes. Being a fairly avid hiker, and pretty experienced, I have a lot of appreciation for lower elevation hiking. Some people just have to be up as high as they can above the tree line. I like the forest too.

My out the door take is that you could have a great time either way. You are right that May will have more pretty snow to look at. Fall gives you more certainty of being able to hike anywhere you feel like.

Good points all around. Thanks!

When I lived in Augsburg, Germany for four years, I did a two day hike up to the top of the Zugspitze, near Garmish, Germany twice.

The first time I did it with my Daughter, who was about 21 years old. We had a guide and stayed in a hutte the one overnight. It was in late June. It didn't snow or sleet at all, but the last portion of the hike was on frozen snow. It was a great hike.

The second time, I did the same hike with my Son, step-Daugher and step-Son, all teens of High School age. The first day the weather was wonderful, but the second day, it started sleeting by early morning. The Guide asked if we wanted to turn around, but we all said no, we want to do it. Well, it sleeted all day, but we did the second day in record time (according to the guide). We were all wet rats at the top (we had gore-tex protection). This was in July.

Not sure where you plan to hike. You said lower-mid elevations. The Zugspitze is the tallest mountain in Germany, something like 12000 feet altitude. We didn't quite reach the top of the mountain, but close. There is a cog train or cable car going down.

Spring or Fall, not sure it is a big difference, but you might hit more frozen ice in the Spring than Fall.

Autumn is Hiking Season in the Alps.
Been there in several places then.
We especially enjoyed this places in autumn
Check out the Kleinwalsertal
A Valley which is part of Austria but can only be reached by car/bus from Oberstdorf Germany

https://www.kleinwalsertal.com/en

hiking in the valley

https://www.kleinwalsertal.com/en/Activities/Summer/Hiking

https://www.kleinwalsertal.com/en/Activities/Recuperation/Walser-Omgang

and we stayed here

https://www-suitehotel--kleinwalsertal-com.translate.goog/?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=de

I'm older. I hike the Valleys and from the lift down. Some of my most memorable hikes in the Austrian Alps and Südtirol happened to be the second and third week in June. You need a Blue-Sky Day. You might have a little snow (higher elevations), but with flowers. I had an easy hike this mid-June in the Hinterhornbach Valley in Austria. I was so happy. I would push my Spring date into June if possible. The lesser traveled route.

The previously mentioned Kleinwalsertal area is lovely, pretty similar to Tannheimertal, but with villages more strung out in a deeper valley. Not a mistake to visit Kleinwassertal.

Yes Tannheimer Tal is great for hiking too

Especially around Vilsalpsee

https://www.youtube.com/watch?v=Ucjfsc755HY

https://www.youtube.com/watch?v=UgHGCt-QYwo

Many of the lifts may be closed in May. You’ll want to look at operating hours. Some are closed for maintenance in the off season. We were in Switzerland in mid-June and some trails had just opened due to the amount of snow. I would choose September.

Thanks very much for all the helpful posts!