A horse is going to have an easier time adjusting from heat to cold. First of all, horses in general are more developed to deal with cold. Second, you can blanket horses for cold, but for heat you really can't do much. Just make sure you have plenty of blankets, and a stall or a big run-in shelter for him/her. I to may be going from California to Colorado in a few years, but I am in a very mild climate in CA (45-65 F year round).
When it is really cold out, you do not want to put a sweaty horse out into the cold. His coat is wet, and although he might be warm at that time from the lesson, the cold is going to catch up to him and he is going to be freezing with the cold coat. Make sure he is cooled downed, not huffing or anything and not hot. You can put a cooler on his wet coat and put a blanket on top of that and put him out in the pasture but you need to remove the cooler once it gets wet and the horse is dry a couple hours later.
As long as you use blankets to keep your horse at a good temperature and your horse seems fine, I bet your horse would be fine going right to pasture boarding, although if there was any grass you would need to adjust him to it.
“Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen.” - Unknown