Most horses CAN jump three feet, unless with an injury. But not all horses can jump 3 feet WELL. Arabians for example, would not be the best choice, as they are not the best jumpers... Large ponies can jump up to 3'6'' pretty well; I have seen those do jumper classes.
I currently have a warmbloodxthoroughbred mare, who can jump up and over 4 feet. I'd say this is the best mix, so good luck!
I have 2 horses right now: Tosca my TBxWB black mare, out of Grand Prix stallion, Figaro. I have my Bay Arabian broodmare, Triana. I jump about 4 feet.