What is the weather like in munich in january?

If I were a real weather frog, I would give a precise forecast. But so I can only refer to my experience: It's rather rainy, quite cold (can be something from -15掳C to +5掳C, that's all more or less around 32 F, plus/minus something), and when you plan to go to the Bavarian Alpes, which are quite near Munich, it will get colder and more snowy the higher (in altitude) you get. January, in Bavaria, is what we call "high winter" ("Hochwinter"), usually the coldest and most snowy month of the year.

Munich itself, as a "city heat spot", usually is less cold than the surroundings; but I wouldn't bet on that. It once took me five hours for 13 km (8 miles) from work to home, as all the streets were covered with ice, and you neither could walk by foot, nor would any taxi driver dare, so everyone tried by car. Most logically, we all gut stuck. But as this happens in Bavaria some 3 or 4 times each winter, we all took it with some humor, and helped each other push our cars out of the mess.

But for wintersports in the Alpes or anywhere else in Bavaria, January is the perfect season.

Munich is at the south of Germany and near to the Alps. So in January is there very very cold.
You can check this on the web also or put on your page the weather about Munich and you can see this daily.