it depends...If the damage does not extent around the whole trunk, then you would be ok...there needs to be some bark left that will allow nutrients/water to make it to the canopy. I had a rabbit one year almost girdle a Seckel Pear...it looked horrible...but because the damage didn/t go around the whole trunk (probably 3/4) it made it... That was 3 or 4 years ago and today the tree is huge and you can hardly see where the damage occurred *the tree will grow around the damage... Now if the damage is completely encircling the trunk, then yeah...you could cut it back at that point (you'll have to, above it will be dead--it may leaf out/flower, but that is only using energy stored in the branches) and it should sprout new branches below that ... Now if you are capable (i've never done it), you could do a bridge graft (google it)... which would also work...

I'm sorry to hear,.. not much can be done to undo the damage.
If completely girdled you might have to cut off below. If some bark remain, cut the torn bark off clean. What I usually do, put some tree wound dressing on [Dr. Farwell's seal & heal] keeps moisture in and prevent from shrinking/cracking wood, healing in better..most here don't recommend to use it. Don't put on anything else...no tar! White wood glue you can use as substitute.
Several bridge graft around the girdled area can help in the growing stage, you could cut scion wood now from these trees and graft when you see leafing out, ...it the wait is too long, then the above branches can be dried out when the tree was girdled completely,...thus, a bridge graft would not work.

A tree girdled half way around or more I wouldn't worry too much,..eventually it will grow in over time on your young trees.

Thanks, franktank, that's encouraging. Perhaps some of the trees won't require intervention. Only a few of them are actually girdled, but most of them are close to that, and there has been significant bark chewed off of all of them. Before I looked at the trees I thought that bridge grafting might be an option, but once I saw how badly they'd been damaged I was scared off from trying it. I did read up on it, but it is probably beyond my skill level. From reading other posts on this subject I gather that it is preferable to leave the damaged area alone rather than applying latex paint or a grafting compound in an attempt to prevent dehydration. Any opinion on that?

Thanks for your suggestions, Konrad. I'm going to go over to my daughter's tomorrow and take a closer look at the trees in light of the input I've received here. As I recall, on most of them the damage extended quite far vertically but might be less than 50% around the tree, and maybe those ones would be okay. Quite a few branches are either girdled or close to it. Would it be best to prune those off?
I'll see if they carry Dr. Farwell's at the local farm store. It sounds as if it would be useful.

Yes, prune the completely girdled branches off,..tree will push
out new branches.

Here are a few photos of some of the damaged trees. The first is a sweet cherry, which looks terrible on one side and not quite so bad on the other (see the 2 views below). We cleaned up all of the lifted bark and took off the girdled branch (farthest to the left in the first photo) and hope that the tree will heal. I'm planning to look for the tree wound dressing suggested by Konrad to treat the damaged areas.

{{gwi:89027}}

{{gwi:89028}}

As you can see, the plum tree below is a mess. It was pretty much girdled, so we cut it off just below the top of the mouse guard. Would it be better to just leave it like that and rely on the new growth that will hopefully develop, or would it be preferable to graft onto it later in the spring? I saved some scion wood from it in case we should try grafting. We did the same thing with another plum and a cherry and we're also wondering about the apricot shown below.

{{gwi:89029}}

The peach tree below is one of the lesser damaged trees, but there are extensive patches of removed bark. The picture shows the tree after we trimmed the damaged areas. That is all we did on this one. Does anyone have an opinion on its chances of survival? Would it be safer to cut if off below all of the damage?

{{gwi:89030}}

This last picture is an apricot. On this one we thought that we would try just cutting off the central leader and leave the 3 scaffold branches, but I realize that this might be risky. The damage on the trunk below those branches does not go all the way around, but it is somewhat more than 50%. There is a patch of removed bark on either side of the trunk with thinner strips of intact bark between them just below the branches. Would it be wiser to cut it off below all of the damage? Thanks for the help so far.

{{gwi:89031}}

Man, I thought deer were bad. I feel for you. The pony must have turned his head completely sideways to make what look like horizontal bite marks.

I wouldn't cut any of the main trunks. If the top doesn't make it, I think they will push shoots from below the girdle anyway. You can decapitate them then.

Anyway, I don't think its quite as bad as it probably looks. The cambium is between the nearly white wood and that dull reddish brown exposed bark. Its the cambium that needs to be intact to keep the live connection from the bottom to the top of the tree.

So its only the white areas where the cambium is gone.

Thanks for the encouragement, murky. We're keeping our fingers crossed and I'll post again later in the year once we see what happens. Even though the damage is worse than it would have been with deer(and they have had a little deer damage in the past), at least there won't be a repeat of the problem because the pony is now in a much more secure area. He won't be getting out again.

Agree, wait and see with cutting,..perhaps next year.
The last photo, it looks like the trunk pretty much had it, the 3 scaffold branches your'e talking about might work,..if you don't mind this low, if it was me, take one of the best branch and tie it upward to the main trunk and make it a leader, you'll have a little bend in it but so what, you could also tie all 3 and select the best later on,.. good luck!

New branches might push out below the bad spot but above the graft, use the best one as a new leader.

We've planted apple orchards at elementary schools, and vindictive (usually expelled) kids would take it out on the orchard, pulling branches off, snapping off the tree just above the graft union, pulling apples off and throwing them at the classrooms. The damage would look horrible, but the trees sprung back and were the same size by the next year. This is evident in topworking new varieties on also; if anything your trees may be delayed a couple years but that's it. No need to shoot the pony, this may be a good time to lop them off closer to the ground and train them to put branches where you want them.

If you do that then you need to cage them in, otherwise, out in your beautiful wooded area, Deer can come by and eat off the new shoot. I always like some extra destruction/protection, a couple of dead sticks are better then no sticks, also good for rodent in the winter.

Could you prune the pony's limbs?

Thank you all for the advice and encouragement. I know that we will have to skip the pony pruning idea, but I think you've given us the information we need to handle the situation with the trees. We did already cut off the worst damaged tree - a sweet cherry (not pictured). It was definitely girdled and thoroughly gnawed, but for most of the trees we decided to hold off and see what happens before doing anything drastic. My daughter was especially sad about the apricot because it was doing so well and had already survived several setbacks. Perhaps that shows its resilience, and it may survive this too. I liked Konrad's idea of tying up the branches to try to create a new leader. Maybe we'll give that a try. They have a fence around the main orchard under construction right now, so there shouldn't be any more equine attacks on those trees once that is finished.