Shibas, apparently. Here is Her Majesty, lying in the snow in -28C (-18F) eating something she dug up. I was wondering how she could lie in the snow for so long when usually she complains of cold feet, but then I noticed she was shivering as she ate. When she finished eating and tried to resume walking, her feet hurt so much she didn't go ten yards, and even after I warmed them up, all she could do was sit and shiver. So, I carried her back toward the car. After a while she felt better and walked on her own, but she wouldn't run. When we got home she had difficulty with the stairs, too, so I carried her to my room, put her under the blankets, and had a nap with her. She seems better now. Crazy animal.
But as to the question of "what kind of dog digs after things": all dogs do. Also, pigs do. And owls. And horses and cows dig through the snow to find food. And bison and moose. And ravens. And chickens. And many kinds of ducks. And bears and racoons. And of course, people. The question isn't what kind of dog digs, really, but what kind of ignorant person would ask such a question.
Dogs dig when they can get something good by digging. And they go after the smell of whatever smells like it's good to have. Why? Because so would you. If you could see that there is $100 buried just under the snow, you'd dig for it too. In fact, we people will grab any resource we find unattended, if we can. I pick up all toques, ski masks, neck warmers, gloves and sweaters that don't get claimed. I have tons of them. If I see money on the ground, I take it. At work, if we see a tool we need, and no one claims it, we take it. We're actually pretty respectful at my work, and try to find an owner first, but in a lot of places you just take what's there and too bad for the guy who left it lying around. Any unguarded doughnut is fair game, of course, and many people will eat someone else's lunch out of the lunchroom fridge, or their roommate's food, even if it's labeled. Those of us who don't are said to have "principles", but that just means we're going against our instincts.
The reality is, all creatures take resources where they can find them, and if they have to do a little digging for it, then they will. Because if something is good to have and you can take it easily and no one will stop you, you take it. Doesn't matter even what species you are, let alone what breed of dog.