Where to see falling snow in early January?

How about Salzburg? or Fussen Germany

Perhaps in the Alps.

Anywhere in the Alps. Or Scandinavia.
You stand an equal chance in any of those areas. Don't expect falling snow every day, perhaps once a week.

I fear a 74-year-old who has lived all her life in tropical countries will not like negative temperatures. She will need some warm clothing.

How about St. Petersburg or Moscow?

Here's the problem. It sounds like the places where you're most likely to get falling snow are not places where there's much else to see or do.

I googled "how many days does it snow in December in xxxxx" and got some good results for averages. For Germany and Austria generally it seems to be about 10-12 days each, and about 2 inches for the month. Note that it could be rain as well as snow and 2" spread over a month is not a lot, could be one big snowfall, could be lots of light flurries.

You may be fortunate, or you may be disappointed. Choose somewhere that you really want to visit and hope for the best.

Thank you for your replies everyone! It's been most helpful.
Innsbruck (Austria) looks quite interesting in terms of things to see and do. I think we might head towards that vicinity and just hope for the best!

If you are interested in baseing in Innsbruck, I would look to the Winter Olympics venues which are at higher elevations than the city of Innsbruck. Seefeld in Tirol was the 1976 cross country skiing venue. Friends enjoyed Seefeld as recent World Cup spectators.
https://en.wikipedia.org/wiki/Seefeld_in_Tirol

Seefeld in Tirol is an old farming village, now a major tourist
resort, in Innsbruck-Land District in the Austrian state of Tyrol with
a local population of 3,312 (as of 1 January 2013). The village is
located about 17 km (11 mi) northwest of Innsbruck on a plateau
between the Wetterstein mountains and the Karwendel on a historic road
from Mittenwald to Innsbruck that has been important since the Middle
Ages.

https://www.j2ski.com/ski_resorts/Austria/Seefeld.html

When will it snow in Seefeld? The next notable snow forecast for
Seefeld is 1cm, expected on 30 September.

salzburg is an easy train ride from Innsbruck. We were there in January and thought it was lovely and Salzburg is an interesting city to visit. Salzburg had just had quite a snow storm and yes, when the train went thru Innsbruck, there was A LOT of snow.

Seefeld in Tirol had last winter 505 cm (16 feet) of snow in total, beating its old record from 2011/12 by 6 inches.

On Labor Day 2017 we had to wait for fresh snow to be cleared to drive the Grossglockner highway. It was rain in Zell am See, though.

Prague. One of the best memories I have is standing in the main square in Old Town watching the snow fall. It's lit nicely, and the pastel shades of the buildings made it incredibly beautiful.

Vienna is also special when snowing, and to me that's the best time to be there. It's in Austria, surrounded by museums, architecture, etc, and easily accessible.

Best bet for snow is being in mountains. here's an example: we live in a high mountain valley, averaging 60" of snow a year, but six miles across the valley, near the high mtns, gets almost twice as much snow as we get at our house. We can see two ski resorts from our house, one on the windward side of the mountains, one on the lee side: Windward side 500+ inches of snow a year, leeward side, 350". So, go to Austria and stay on the windward side of the Alps. I suspect that would be Vienna, Melk, Steyr, Salzburg, Hallstatt, Bad Ischl, Bad Ausee, Lofer, St Johann im Tyrol, Zell, Zell am See, Badgastein, Feldkirck, Worgle, Hall, the Oetztal(Solden), and Innsbruck.

To simplify my earlier comment-- best chance for snow is in the mountains. What you do when it doesn't snow is sight see. Best way to do that is the Inn River Valley from Salzburg to Switzerland because there are mountains on both sides of the valley, and lots of towns to visit in the Valley and nearby. Get a Michelin Green Guide Austria for details. Also, on good weather days , do some mtn sight seeing-- spectacular views. Some of the best scenery in the Alps is the three south running mountain valleys to the west of Innsbruck.

Scandinavia is not a bad choice, plenty of towns that have a high chance of snowfall in January.