Well it is up to Bethesda, it is their series now. If they did introduce horses, I would hope they have a story about how traders brought them in from some remote region. That they are costly and expensive and not to mention there wouldn't be anyone who really knows how to take care of them or breed them. But people could learn, old veterinary books and so on. Maybe even have someone say "keep them away from radiation, radaway isn't cheap."
It would be nice if they did it right. Not just "hey there has always been horses but we just haven't bothered to show them till now." I know it isn't in Bethesda's nature to explain things but I would hope they learn to start doing that. If they brought horse back they should.
There is also the debate on cats being extinct or not. I would like to see cats because I don't believe they are gone, in Fallout 2 there is a lady talking about owning a cat when she was young, so we know they survived the Great War.
People also normally confuse the words extinct with extirpated. Extinct means gone completely, nowhere to be found on earth. Extirpated means it is wiped out in one area but still exists in another. So if lets say the people of the Core Region for some reason went around and ate all the cats or horses or what have you.. that doesn't mean those things can't be alive in Mexico, or Texas or in some other part of the world.