In TN, neighbor owned an exterminating company; his suggestion would be expandable foam and steel wool. Seems mice don't like chewing on metal (they destroy copper...my experience using copper mesh), but steel wool rusts. So what he would do to close up holes in houses, was to foam one side, go to the other side, fill it with steel wool, then seal up that side with the foam. Or shove the steel wool into the home and then foam on both sides.
I did that and the mice didn't come through the hole again. They had actually chewed through some of the foam, but stopped. Then they went and found another hole to come in through. Learned that living in the country, with fields all around, it was next to impossible to keep the little buggers out, but a few weeks after the cold spell and after they moved in, good traps took care of the problem, till the next fall.