Things we like to do:

• Ski. Lift tickets and rentals are expensive, but smaller mountains can be done for ~$100/day. Having your own gear is cheaper (and more comfortable) long term. Some places do seasonal rentals with inexpensive options to buy at the end.
• Find walkable towns. I love drinking hot coffee outside on cold days while wandering in and out when it gets too cold. You don't have to buy anything, but you can find new interests.
• Hiking. It's warmer than you think.
• Photography. It doesn't require fancy gear. Use your phone. Get close up, take photos of friends, create weird scenes.
• Walking on ice. Potentially dangerous if you don't know the lake, but some parks allow/semi-encourage it and ice fishing huts are a good sign.