When I used to complain to my Mother that I had nothing to do, her stock answer was to clean my room.
Turns out that it really was not a bad idea. I usually ended up finding things that I'd thought were lost forever, and organizing stuff that really needed organizing. After it was all done, I always felt great and made a resolution to keep my room sparkling clean from now on. (That never lasted more than a day.)
Indoor days are also great for goal setting and making plans for future events. It might be too cold to go out right now, but how about organizing an outdoor event for later when it does warm up?
Is there a place to go skating or tobogganing near by? A winter picnic after a little outdoor activity can be a lot of fun. You can make hot chocolate in a thermos and precook weiners at home. When you are ready to leave, put the cooked weiners inside a crockpot, cover with boiling water, tape the lid down tight and place crockpot inside a cooler with towels stuffed around it. It will stay hot for a couple of hours. The hot dog buns, ketchup and mustard can be thrown inside the cooler on the top of the crockpot as well as some cups and napkins. Make some rice crispy treats for desert and you have a great outdoor activity complete with lunch.
How about doing some baking? Homemade treats can be stored in the freezer for later enjoyment if you don't want to eat them all now. The whole family will enjoy your efforts.
Cold days are great for playing board games with friends or having a movie marathon. Of course you'll need lots of popcorn, and maybe you'll need to spend a little time getting the rumpus room or living room straightened up before inviting guests over. Your parents will certainly appreciate your consideration and initiative, especially if you clean up after everyone goes home again.