We live in the no-snow (rain rain rain... wait... yep, rain) part of the state...So we drive to the Pass for snow stuff. Which means our excursions are planned.
In general, we're snowboarders. We also dabble a bit in dogsled. But that's because our lab is a husky in a Labrador suit (doesn't swim, doesn't fetch, but mushes for days).
The few times we actually LIVE in snow... We spend about 10 hours a day outside, and 4 inside. Unless its 20 below. Then its just like living in perpetual rain: inside all the time except when schlepping from point A to point B (can you tell how much rain thrills me? :P)
In the snow... As long as you're warm and dry (aka have quality gear, and its not frostbite weather or blizzarding out ), its like summertime on a giant soft beach. You can literally do just about anything. Including picnics, kites, hikes, building, tag, volleyball, read, etc.). In fact, beach people TEND to make really great snow people. As long as you've got good gear!!!
Do NOT skimp on snow gear. It's the difference between LOVING it outside, and being miserable. This means gortex for kids, as well. So they don't overheat or freeze. Which (at apx $500 from nose to toes) gets EXPENSIVE. EXCEPT, very few people buy new or buy new FITTING clothes. You'll find kids snow gear in October "swap" type gatherings... Where prices are pretty standard... Apx $100 per top or bottom. And then next year, you sell yours for the same prices, and buy someone else's.
Quality gear lasts for about 10 years, but will need to be washed with TekWash (detergent ruins it), and rewaterproofed once a year ($10.
That... Or buy new in BIG sizes, and get 3-4 years of wear out of them. Cuffs usually cinch/Velcro, and waists are adjustable... For just this reason. Kids not only don't care, but often WANT the slinky/baggy look (easy to move in) when they get older. LOL... So you end up buying "too big" even when they're done growing.