The native animals do fine most of the time. Bison will brush snow off an area to find food. Cattle will stand there and starve. Mule deer prefer hillsides, where the wind blows much of the snow off. Whitetail deer prefer creek/river bottoms, where there's brush to keep snow off of browse (and will browse on trees if they have to).....and both will raid hay. Elk like the higher altitudes, but will move down the mountain sides as snow gets deeper up high. Moose.....go wherever they choose. All will make beds in grass, usually on the lee side (of shrubs, hills, rocks, trees) to avoid the wind. The winter fur insulates them pretty well.
The deer are more wary of the unfamilar/unexpected. They've been coming through/living in the fields below their entire lives. There aren't a lot of predators that can take them down (besides humans). Dogs aren't allowed to harass the deer (easier to hunt in season) and other deer predators are also a threat to cattle, horses, and sheep, so when they do show up, get removed fairly quickly (whether Fish & Game traps and moves them or they simply get shot depends upon the circumstances at that time). We've never hunted deer on our property, so they feel pretty safe in that regard.
A few communities have the entire herd living in town. They figured out that cars are the biggest threat...and getting hit by a vehicle at 25 mph....They're more likely to stand back up and trot off while you're still looking at the dent in the front. Gardiner (entrance to Yellowstone) has ELK in town much of the year, and West Yellowstone has had to get the kids in off the playground due to BISON strolling through during recess.
Shy and skittish......no more than any animal vs the unknown.