As WastelandShadow pointed out Chris Avellone has said the Horses in http://fallout.wikia.com/wiki/Horse "To me, that picture in the comic was an error (no one noticed it until too late) and that "it was never my intention that there were any horses." He went on to say that "there were parts of the New Vegas design where we specifically removed the mention of horses from certain narrative points (one of Raul’s stories originally referenced horses, for example, and we cut them because we didn’t want to imply horses still existed)." -Chris Avellone.
Horses can't vomit and even a simple things such as seasickness can kill a horse. So if they encounter radiation they will get sick and die easily. So horses wouldn't last long after the Great War and if Bethesda makes another radioactive hell hole for a setting, then no it wouldn't make sense for them to be alive.
That doesn't mean they are extinct, but to me the chances are they aren't around anymore. Plus I don't like the idea of riding around on a bullet sponge horse and not to mention they aren't ATVs (all terrain vehicles) and people will complain they can't use them as such.