Yes a reefer can be turned off and just have the fan as far as I know.
But if you got a load then you would have to load the horse in the front and the cargo in the back next to the doors. Otherwise you have to unload the horse before you unload. Then how long will it take your driver to make it cross country, what about feeding and water?
I think I would spend the money on a shipper rather then spend the hassle converting a reefer into a horse stall and worrying about delivering a load on top of that.
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.