If I were you, I would not let the weather keep me inside. We invested in some good quality winter and rain gear for our boys (and ourselves!), and I'm so glad we did. It is so nice to not feel restricted by the weather anymore. I still wouldn't go out to play if it was colder than 15 degrees, but that's not the norm where we live--it's usually about 20-35 here (don't know what the weather's like exactly where you are). Snow is a great thing to play in with a spirited toddler! It takes lots of energy to walk through snow, and it can be manipulated, rolled around in, jumped in, etc. We've only had one good snowfall so far this year, but we had a lot of fun playing in it while it lasted.
www.patagonia.com sells capilene long underwear for adults, kids and babies that will really keep you warm. I don't leave home without it! it is expensive, but will most likely last two winters.
I cannot imagine being cooped up inside all winter with ANY toddler, let alone a spirited toddler!