You can try to take regional roads, but cycling paths you can't be sure to use, because not free of snow. So important cycling paths like Danube cycling path (Euroevelo 6) and Bodensee-Königsee-Radweg (Berchtesgaden - Lindau, but is more critical). If taking the roads, you should know, that there is a lot of snow mud at the road, even smaller lanes, because snow is at the side and cars splash mud. Even sometimes landscape is touched by intense dust, especially close to water.

Of course, nobody can tell you a serious weather forecast. January can change within a few days totally. I had once a short trip in Northern Germany, beginning with ice, snowy conditions, but sun, -8 °C, most cycle paths closed, not ridable. A windy, rainy day with 4 °C, all snow nearly snow smelling, but ways aside roads are muddy, finishing with warm weather and sun, 8-10 °C. You get milder climate close to the rivers and lakes. So maybe EV6 is an option, but sometimes changing to the road. Upper Danube valley is more critical than lower parts. You can change later easily from EV8 at Stein am Rhein to Zurich. Cycling paths in Switzerland will be in better conditions than in Germany and maybe a lot them free of snow for local commuters. In most sections you have the possibilty to change to a train.