Get a sled to pull behind your snowmachine. You can carry a lot more than on the back. Also what kind of snowmachine do you have? A lot of them aren't designed to pull a sled and you will spend a lot of time stuck if you don't have the right snowmachine. When snow gets that deep I don't set in the dirt, I go to making sets in the snow, bedding the trap in the snow, usually on wax paper, cover with wax paper and then snow if it isn't going to snow soon. But I prefer to just put wax paper over the trap and let it snow over naturally if it is snowing or is going to snow soon. No matter what you do if you move snow it tends to freeze and set up hard. Try and find places where the wind doesn't drift the snow to set. Many recommend setting under trees where traps are protected from the majority of the snow. I do that some but I have found that setting under trees here it often warms up and the snow drips out of the trees all over your trap and freezes into a hard crust, setting in the open you will get more snow over your trap and you will have to reset it because it has too much snow over it if it snows a bunch, but it doesn't usually crust over as hard. Ideal is shaded places that aren't actually under any trees. Also black traps collect heat and melt out, especially if they catch any sun. White painted traps work much better setting in snow.
If you have a lot of wind you may find places where it blows all the snow off and leaves bare ground. In those places you can set in the dirt and keep traps working, but dirtholes tend to catch snow and fill up, flat sets or pee posts are more weather resistant.