I had an unfortunate experience with a rescue horse this summer that left me, while thankful that there are rescues out there, never wanting to adopt a horse from an organization.
Of course the horses need adopters but seriously, I don't want to encourage the ridiculous one-up-manship-type politics that seem to plague the rescue game.
If you want to "rescue" (very noble, I commend you), I bet you could find a horse that needs an "upgrade" without any rescue-related strings.
I found my Lacey girl through a common friend and I suppose you could (depending on your interpretation of "rescue") say she was rescued in that there was already an appointment for for euthanization scheduled for not even a week after met her which would have happened if I hadn't met her and "clicked" with her (she's a "hot" mare that needs specific handling and she's "old' - not a great combo for selling). She also had some serious training issues and a bunch of mental issues that just needed correct handling to get through.
I don't like to think of her as a rescue since I really feel like she rescued me more than I rescued her. BUT, in terms of an upgrade, 5 more years of life, so far, is pretty good!
Anyway, bottom line, you don't need to use a rescue to rescue a horse. :)