in 2000:

"A horse apiece" means, as you supposed, "more or less equal" or "six of one, half dozen of the other." Field researchers for The Dictionary of American Regional English (DARE) first heard "a horse apiece" in 1980, but the phrase is undoubtedly much older. A similar phrase, "horse and horse," dates back to at least 1846.
According to DARE, the logic of "a horse apiece" may come from an old dice game called "horse" in which two players who have each lost a turn are said to be "a horse apiece." Or it may just be a variant of "horse and horse," describing two horses racing neck-and-neck down a racetrack.

Tom_MN posted to the A Way with Words Discussion Forum with some geographical boundaries:

I have a lot of funsaying once at a party in Minnesota, and a 70 year old man perked up and said that people in Minnesota used to say it, but that he never hears it anymore.

A:

It's related to the game of Bar Dice, which is mostly played in the Midwest.
Bar Dice plays somewhat similarly to poker. Players roll multiple rounds and try to get as many of a kind as possible. The player with the best hand in each round gets out of the game, since it's a drinking game and the goal is not to win but to not lose. The last two players roll best two rounds out of three, and "a horse on me/you" is a slang comment for losing one of those rounds. If you lose two rounds,