Would you be comfortable giving him a little sedation before they leave?
I understand the reluctance to introduce a new horse in snow and ice but I would prefer that approach to a horse alone with nobody to huddle with in the cold. Lots of piles of hay should keep the shoving to a minimum.
If he doesnāt mind if they leave he may very well live alone with little anxiety. I would either have him in a place he canāt see them leave --or-- take him out for a ride if you think they will be anxious and a mess when loading them to go.
Not all horses do well with goats and he may not take to another horse that easily either. Give him a chance to settle and then see what you need to do. If possible have a place with secure fencing if he comes unglued ( round pen or similar).
I skimmed so apologies if this was mentioned further up. I had to do this one winter and keep my horse alone on my farm for a little while. I called up the local horse rescue and asked if I could foster a buddy for her for a couple of months. I paid for the pasture-mateās feed and trim, the rescue sent her with medication she was on so it wasnāt a completely burdensome amount of money for the trade off. When I was able to move my mare to a new barn, I took the rescue horse back and all was well.
My mare wasnāt calling for her friends or acting anxious at all when by herself. However, I realized a few days in she was very tired and I donāt think she was sleeping without the comfort of another horse in the pasture.
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I wouldnāt bring a rescue horse to the property without being set up to quarantine before turning out. Copper, That was a good catch to realize your mare was not sleeping well.
OP, There may be no problem. I donāt know that heāll be scarred for life by watching them leave. Depending on how far away you can ride him, it sounds as if heāll be hearing them scream anyway.
You know him best. Perhaps ride him or, if he enjoys being groomed, give him a good groom while they leave.
I agree that a goat is probably not a good idea, especially since this is a temporary situation.
Brilliant solution! 
I agree with trying to find him a buddy, even if it means introducing in the snow.
But if you just really canāt/donāt want to - you could try Valerian root, Iāve had great success using it for herd-bound horses, and itās really easy to wean them off of it without regression back to herd-bound-ness. I give ~2000-3000mg per day.
