A budget horse is pretty much the worst possible mount.1) 2)Rumors have it that the budget horse eventually dies and is replaced by Son of a Budget Horse.

The Budget Horse might be useful if the rumors are true, because the Son of a Budget Horse is supposed to be totally awesome.

Budget Horse is sold to Contestants at the Mike's Chop Shop located in NewHome for two Cigarettes.
Mike's Chop Shop buys Budget Horse for one Cigarette.

1)
You might get a better deal buying a Magical Mystery Meat Mount, depending what effect you prefer and how long you want it for.
2)
And don't believe what you may hear.. He's a horse.. just call him 'horse' or whatever. Not Tim. Nope. Not at all.