It could be an allergy to a number of things including feed, fly bites, nettle stings etc. However, it could be caused by the stress of the move. Also, they might be heat spots (don't know what the weather is where you are). If they are painless I wouldn't worry too much.
Good luck with the vet.

It could be bugs. Can you find a bite mark in any of the larger bumps? It would be a tiny scab usually. If that's the case you just have to invest in a good fly sheet. If not, I'd lean toward allergies, especially since you've moved him to a new environment. Bedding changes, feed changes, new pollens, molds, etc can trigger the reaction, hives, that you've described. To figure which allergen is causing the reaction, you'll have to remove each allergen one at a time. I'd start with bedding. Give it a week, see if the hives resolve themselves, if not, move to hay, then grain (if that was changed also). Remove one allergen at a time until the hives resolve themselves.

I have done this before, I ended up having to move my mare because even after I removed hay, grain, bedding, supplements, moved her to a different stall, changed her from turnout on pasture to a dry-lot (in case grass was the problem) she was still covered in huge hives. Within 48 hours of removing her from the boarding facility, the hives were gone.

Depending on how bad the hives are, your vet may want to start your horse on anti-histamines and possibly steroids to help reduce the hives and inflammation. Your vet may also want to do skin allergy testing. I chose to move my mare instead of putting her thru the testing as it is painful If you've ever had skin allergy testing done on yourself, it's the same process.

Sound like allergies. We have a coupe of horses here that are allergic to some thing in the turnout pasture and have to be given benadryl( as prescribed by a vet) any time they are out there. So far we have been unable to identify what exactly is out there.
Good luck with the vet that will be your best bet