They aren't draft horses, they are riding horses, but you are right that they are not light Arabian in type. They are standing in a position that would make them look the most blocky, with their heads up.
All I know of the other horses is that Viggo got very attached to his and bought it. (he apparently also bought a young girl, according to the writing in the story ;~D)
More on Viggo Mortensen and his Horse - Xoanon @ 10:47 EST
After the principle filming wrapped for Lord Of The Rings, Viggo Mortensen (Aragorn) travelled to a farm in Northland. The farm had been "taken over" by the production so they could do all the horsey things they needed to do for the film. Apparently Viggo turned up in a limousine dressed in boots with a full length weathered coat and scraggly long hair. With him was the girl who had been hired to tend his horse; the one he had primarily ridden in the film. He then proceeded to negotiate a price for the horse and also one for the girl. I do not know the price but it was quite a princely sum. The intention was for her to travel to the states to continue caring for the horse.
Attached is 4 pictures of the horse ridden at a horse trial by one of NZ's foremost show riders.