I agree (although on a regular or minimally mutated one) but I know many disagree with me. I blame Obsidians timeframe, that they didn't have time to test horses ingame with balancing and all that.
My explination is that after the Great War, horses migrated north to colder lands, to Canada. And then I hope Fallout 4 takes place in the northern USA somewhere, close to the border, so that horses maybe would have migrated down abit during these 200+ years, and being domesticated again. But I think the NCR would have fit perfectly with cavalry, they would so remind me even more about WW1 brits than they already are!
Edit: And don't come with any "we haven't seen horses before so therefore they don't exist"-[censored]. They could be a regional creature, just like bighorners and cazadors. They were never in any other fallout game, or even mentioned. But they exist in FNV, and no one is complaining.
Edit 2: Maybe some rare encounter like http://farm1.static.flickr.com/3/3415855_7d52aefe5c.jpg, for a nordic mythology reference <3 (yeah, I know, but it does look like a horse with eight legs)