Snowbiking was brand new to me last year after having ridden sleds and dirt bikes since I was a kid. I've found that I have to un-learn a lot of things learned while riding sleds and dirt bikes. Here's a few things I can think of:
1) Don't worry about tree wells -- they won't suck you in like when you're riding a snowmobile.
2) The sidehill is your friend. It's ridiculously easy to sidehill, you just sit there and pick as steep a line as you want. And you can sidehill while going downhill, which is really hard to do on a sled. It makes it extremely easy to go as slowly as you want when dropping down steep slopes.
3) Because sidehilling is the preferred way to get places, you look for completely different lines than you did when you were on a sled... every riding area that you've been to a million times is all new.
4) I've found that when I'm in tight trees I have to make sure I pin the throttle and keep some momentum when I make tight turns, or else I WILL kill it and fall down.
5) Get in the habit of keeping your feet on the pegs -- don't rely on putting your foot out to hold the bike up when you're in tight stuff or you're stopping, because most of the time, especially in soft snow, your foot will just sink and you'll fall over. This is another reason I love the sidehills -- it's a lot easier to get a fairly solid foot on the ground on the uphill side.
That's all I can think of for now... I'm still new to this stuff and am learning and gaining confidence every ride. Snowmobiling and dirt biking haven't been this fun for years.