I've seen many people hunting ptarmigan with scoped .22 rifles that they rest on the snowmachine seats. Good for them, I don't like that style at all.
My group of friends all hunt on skis with shotguns and dogs, flushers and pointers. Skis are much MUCH faster than showshoes, and pretty necessary if you're going to keep up with the dogs. I personally know about 5 people who were snowshoe hunting, but only a few days per winter because it's so shitty. They bought skis and now we go all the time because it's fast and fun. We've tried snowmachining in deeper to the backcountry, but gave up, since it's such a hassle. My snowmachines have sat unused for the past 2 months. We usually cover 7-12 miles per hunt on skis and that's plenty to get away from any crowds without needing a sled, even right next to Los Anchorage.
Here are some pics from this past month in south-central AK. Snow sdepth range from inches to many meters. Temps from 0F up to 15F.