For what it's worth......I've never had a mouse-girdled tree when I've kept grasses etc away from the trunk. And I've not used screening on the trunks. Ground herbiciding is very effective not only in preventing this but also in getting maximum growth out of your trees each year.
That may hold true in places with little or no snow but, the voles will tunnel under the snow crust and girdle trees whether the ground around is clear or not. It's best to spend a few dollars for protection. They'll eventually find them.
sorry.. folks. I have been so busy with work. I looked at them this weekend. One is girdled all the way around. The others are partially. I seriously hate mice and voles or anything that is chewing them. but, I have no one to blame but myself. I think i am going to try a bridge graft. I will say that I have some shoots coming up from the roots of another tree and I might snip them and try it. I wish it was on that tree, but it's not.
My first chestnut was girdled all the way around about two feet up. It came back below the wound. Lost the top which was about two years old. Two years later, it was right back where it was before the varmints got it.
Start thinking fox habitat. They like to keep those things in check too, that is if you're not concerned about your bird population.