I have dealt with a rescue organization before and the experience was nothing but negative. I don't want to go into details, but I had to hire an attorney to be able to keep my horse. I know there are some good rescues, but for the most part you are asking for trouble in my opinion.
You can go to an auction and buy a dirt cheap horse. A horse that might otherwise go to a kill buyer. Therefore, you are rescuing a horse. The only difference is that this horse will actually belong to you. You won't have the threat of having someone come out and check your property only to take him back if there is poop in the stall or having issues with the rescue if you want to sell or rehome the horse.
IMO, there are many rescues that are wolves in sheep clothing. Besides, why would you pay an adoption fee when you can go to the auction and save a horse.....and own him outright.