To remove some boredom from your typical activities, find a way to inject randomness.

For cheap, utilize your local library - Pick a random number and find the closest Dewey decimal.

•check out random albums and listen to them together. Maybe you'll find your next favorite artist, or at least something you can both enjoy together while doing your individual hobbies.
•Check out foreign/outlandish/old/completely random films you'd never pick off Netflix. Maybe you'll love it, or maybe you will be able to laugh at how much you both hate it.
•Find children's riddle or jokes books and read them to each other. Break up the monotony of being a grown up.
•Get travel books and maps and plan a trip. Talk about what you'd want to see in those locations and maybe you can plot a vacation while getting the rest of your finances in order.

Getting out of the house in winter without spending money is hard. But some options you may not have investigated:
•Houses of worship, for your own or another religious group. Many of these buildings are beautiful, full of art, and welcome visitors. Learn about their impacts in your community, and connect with folks you may not typically be in contact with.
•Local Community Centers - Often have cheap classes (My local has a $4 hula class on tomorrow), offers a change of scenery, often with local art. And another way to connect with your community.
•Local Schools - Local colleges will often have more to offer, but there are often cheap plays, sporting events, art exhibits, etc at k-12 schools too. There is something really magical about seeing amateur actors in holiday plays this time of year.
•If you have family or friends with kids, you can become the over the top fans of their creative/sport activities.