Gardening

As-is, yes, it's essentially a goner. I would expect the existing growth to die off and a bunch of water shoots to emerge from below the wound. You could try to prune one of these shoots into a new central leader and cut off the old stem. You could try to get creative and cut strips of bark down to the cambium from the section above the wound and graft a bridge across the wound. But I would only do that if there was a specific attachment to trying to save that particular tree.

IMO you would be better off replacing it and getting trunk guards or making your own with aluminum window screen. Getting a healthy replacement planted will get you a healthier and bigger tree faster than trying to save what you have.

https://livetoplant.com/step-by-step-guide-to-treating-girdled-tree-trunks/

In my non-expert opinion, eez dead. A lost cause but I can't tell if the girdling goes all the way around.

I'm an arborist and I will confirm if it looks this way on the other side too it's a goner.

It’s a goner. Next time wrap the base with hardware fabric.

The tree as it is can't be saved. It is fully girdled and it with die as is.

You can either purchase a new tree or have a little fun over the next few years.

The top of the tree is likely still alive at this point. So you can take cuttings from the top an with some rooting hormone start new trees from it. You can plant these directly into the ground once established.

The root is a different species and is also alive. If you cut off all of the grafted section the rootstock will send up new growth. Then next year you can take cuttings and grow the rootstock for a year.

In 2 years you can graft new trees like what you have. In another 3-4 years you'll have a tree the size of the original.

Get cardboard trunk guards or some chicken wire and make a barrier. The cold is certainly not going to help, but see if it starts sprouting once it warms up and gets some sun. If it gets buds, it'll be fine.

Keep those trunks protected though until they get a few inches of width.

That rodent has got a vicious streak a mile wide. It’s a killer!

Hard to see anything from this picture, but yeah you can't really fix damage to trees, only let them heal themselves. All you can do is protect it and give it all the resources it needs to heal (water, fertilizer, light).