There is nothing wrong with hanging a bike up. But, both you and your bike would be better off if you don't. Instead, keep riding.

When I lived in the "Great White North", I'd ride my bike in the morning when the windchill was ten below zero. Not fun, but doable. And, on sunny days when the temperature was a balmy twenty degrees, riding was very enjoyable.

Here in Texas, I have a friend who only misses his daily ride two or three days a year. Obviously, in North Dakota or New Hampshire, riding 350 days a year is not likely to happen. But, even in those states, there will be sunny, dry afternoons in January and February when a ride would do both you and your bike a world of good.