The comic [i]All Roads[/i] by Chris Avellone - one of the lead designers for the Fallout games, and compiler of the Fallout Bible - shows that horses are very much still around.

[url=http://img3.wikia.nocookie.net/__cb20101227035025/fallout/images/9/98/FNVAR_Horses.jpg]Here[/url] is a picture of said horses in the comic.

Considering that NCR is very well-off, with as many as hundreds of thousands living in NCR (formerly known as Shady Sands) alone, I think it is perfectly acceptable to assume that horses have been bred. Why would the NCR give their soldiers the last few remaining horses on Earth without breeding them first? They probably wouldn't. The fact that they are seen on horses, I think, is proof that horses were bred and used as cavalry.

EDIT: Just read the link you provided. [s]Their argument against it is "it's probably a mistake". That is a bad argument.[/s]

EDIT2: Read the trivia and Avellone admits it's an error. Welp. 'Guess I'll show myself out. Not sure how interested I'd be in playing another unit that is more or less the same as the rest, and going with horses despite canon would probably bug me too much.