(After plenty of googling, I'm starting to think the answer is no.)
I had adjusted our route to avoid the mountains, but the forecast is for snow anyway. So I'm back to needing to figure this out!
Gemut.com says "The good news is if you’re not in the mountains, your chances of actually driving on snow are pretty small. And when it does snow in Germany, roads are quickly cleared."
Doe that mean that the law applies only if you're actually driving literally on snow, as in there's snow on the road? But that generally the roads are cleared, so it's OK?
More specifically, we're planning to drive from Munich to Rothenburg and then the Romantic Road from Rothenburg to Fussen in about two weeks.