When its slushy like that, the best thing to do is pack the snow down, not remove it. If you pack it, the water will soak the snow, and then freeze, making a nice base for your hut.
Snowshoes are great for doing this too!!! And they'll keep your feet out of the slush!
Did I mention I hate slush??
Good going getting the kids out, I'm sure they had a blast!!
Sinker