A.H.
I say, bite the bullet and pay for really warm, waterproof stuff for them and then go outside and have fun! My son goes to an all-outdoor preschool and they have a blast no matter the weather, but the real key is the school is very clear about required clothing. They have wool long underwear, hats, mittens, rain boots, snow pants, snow boots, etc etc. That makes all the difference. I have found some great stuff and garage sales and consignment stores.
I know it's not always what we feel like doing, but I've rarely regretted spending time outside, and often wished I hadn't just stayed in due to the weather.