Originally Posted by Miakoda
It is "bobtail".
Back in the day, and even today, the tails of draft horses and carriage horses are docked (aka bobbed). It was done to prevent the tails from getting caught in the equipment and subsequently ripped out. At some point it also became fashionable, but its roots lie in practicality.
Oh, and bells were often woven into the tails, and sometimes the manes, of the horses during winter time.
I should have been clearer - I know it's bobtails now, but I just thought it was funny that I actually had it right as a kid, and was (wrongly) corrected lol