This is such a bad idea. The only time I would ever consider doing that is if you're buying a foal and its from someone you know.
This just reminded me of something. One of my friends did buy a friesian foal just from pics and videos, it should have been fine, you can't tell much about a 6 months old anyway, and there are people buying friesians sight unseen pretty often. Little foal traveled from Netherlands to Sicily (almost 1500 miles).
When he arrived, first vet check revealed that horsie had a broken little bone in his rear leg. Probably happened during the long travel. My friend didn't have the heart to give the foal back and ask for another (the seller was serious enough that he could have done that).
He had a vet who believed that the damage was small enough, and the horse young enough, that it could have been fixed. Little friesian spent months and months closed in a stall with daily shots and medication. He recovered eventually, and is now the stunning black horse that my friend wanted. But, with the money that went into him, he could have bought 2 adult, well trained and sound horses (even friesians).
This just to say, long distance + you don't know if the horse will be transported with proper attention can lead to injuries even if the horse was perfect from the beginning. It might be work if you are a breeder (it's a risk you accept because you really want good bloodlines) and if you do big shows (and possibly, you paid the horse enough that you cared that transport is as perfect as possible).
It is ok to let a trusted trainer to look at a horse and buy him for you, but buying a horse from far away when you have limited experience is not good.
I know about seeing ads of awesome horses that you want so much, but it is better that you keep looking in your area, when you will have your trainer and your vet to help you, and to keep you away from "wrong" horses.
It is easier to renounce to buy a horse, than it is to send back a horse that you feel you already own. Especially your first horse.