what adventages would a tall horse have as a plains dweller?

On the early American great plains, prarie tallgrass was - and in a few areas, still is - very tall indeed. A tall horse would be better able to make it's way through that, keeping a wary eye out for predators and relying on long, powerful legs to carry it out of danger. Other than that, there is no real advantage that accrues to the taller horse.

A taller horse would probably be faster as a result of longer legs, stronger overall, and bigger in appearance, deterring potential predators, who are very selectful of their targets so that they minimize their chances of wasting energy or getting hurt.

If you're talking about a male horse, it would also look bigger and so attract more females and drive away other males. This is very important because often one stallion will control a whole group of females, and the smaller males will have none. If you're talking about a female horse, it wouldn't have such a mating benefit, because female horses have the power of mate selection, and would find a good mate no matter how large or small it was.

A better view of the surroundings is also beneficial, but since horse eyes see mostly below and in front of them, instead of straight ahead like a human's, probably not as big of an impact as you might think, unless it was ridiculously tall. That's partly why a horse stands on its hind legs when startled; it sticks its head up so it can see what's right ahead of them. I imagine that most of the benefit would be just derived from that's it a larger, stronger animal.

Tall Horse=Long Legs

Long Legs=Better Running Speed

Better Running Speed=Bolero or Not

or not

The major advantage that height would give a horse (or anything for that matter) is the ability to see danger (predator or fire) farther away than an animal that is not as tall as the prairie grasses. Of course, being taller lets the rest of the world see them from farther away as well.