Just because its colored, doesnt mean its Paint. Lots of breeds have that coloring, its called a pinto...
Id venture to say maybe a Saddlebred, though maybe not the typical look. They have some pintos in the woodpile. The Forelock, did you cut it? If not thats another clue, saddlebred people tend to keep that shaved for a clean appearence.
Some saddlebreds do gait, I have one, but not all of them do. Not all of them have the high knee action either. I have one of each.
Either way, thats a cute horse. Have fun with him.