If you get a big batch of snow a lot of times the animals will try and lay low for a day or so and 'wait it out'. If it doesn't melt in those first 24 hours or so though, they get up and are moving all over. Like steeliedrew mentioned, they often head to the timber or older reprod, where the snow doesn't penetrate.
All that said, a light snow doesn't usually change their habits much, you need a good 6"+ from what I've seen.