Ha, our German Shepherd loved snowballs too. He would chase them and chomp them for as long as you were willing to throw. Then he would proceed to pee like a horse for the next few hours. We had to not throw snowballs after 4pm!
I think that cross breed would be fine in the snow. Most dogs do not like boots anyway. But just keep an eye on him and check his feet.
Our German shepherd loved the snow. He used to nap in a giant pile of snow and when you called him he looked at you, turned his nose up and just stayed there. We had to go out and bring him back in.