There are gaited Morgans, so he might well be a Morgan.
If he has a rack/amble/stepping pace/shuffle sometimes?
Pay attention to what you are doing when he goes into it, the speed, your aids, and the terrain.
Get him moving out at a walk, and when speeding him up slightly, try "shaking" that head a little, by lightly taking up one rein and then the other.
Horses make me a better person.