RxPhantom The coloration, elongated snout, and antler shape definitely mark Morse as a moose.
https://en.m.wikipedia.org/wiki/Moose
Reindeer (aka Caribou) are generally more of a silver/gray color, have a smaller body, and a proportionally larger set of twig-like antlers instead of the open style antlers that moose have.
https://en.m.wikipedia.org/wiki/Reindeer
For Morse's description I think the "I ain't pullin' no sleigh" is a direct reference to not being a reindeer, but I could be wrong on that. He's also a bit taller than almost every other character which makes sense as moose are HUGE.
Still, Morse dressed up as a reindeer would be hilarious, ha ha.