I've had a similar problem in an even colder environment, and other people in my building have had mold problems from it.

So, first thing; many single family homes or row houses will have forced-air heating systems that constantly circulate air. Those will have dehumidifiers on them. When I moved to my building, it was the first radiator-heated place I'd lived in. Radiator heating turns the unit into a sort of sealed box as far as humidity goes. There's a handful of techniques to dealing with this, and many of them didn't occur to me when I first moved into a place that needed them from the combination of uncirculated air and low temperatures.

As others have suggested, a film creating a barrier between (humid) air and the cold window will both prevent condensation build up and significantly improve your heat retention. Most buildings that aren't single family homes (and many that are) have shit-tier windows that leak heat badly and make condensation and heating problems much worse than they have to be.

Managing humidity can help, but not fix the problem. Keeping your bathroom door closed and fan on when you're showering or bathing will cut down on the added humidity. When you're boiling water for food or releasing pressure in a pressure pot, you'll also be getting humidity; opening a window for a few minutes can help vent it.

In my experience, the best way to both prevent condensation and remove any that's built up or frozen is just to point a fan at your window. A dehumidifier can keep your unit drier, but I don't think it'll remove window condensation entirely. On the other hand, just keeping the windows clean doesn't mean you've got the humidity low enough to prevent mold. But, as far as keeping the windows dry, a couple of $10 fans should solve your problems.