When animals get crossed, the male gets the first half of the name.
Male lion + female tiger = liger
Male tiger + female lion = tigon, etc.
So if it was a male caribou, it would be a cariboose. If the moose was male, I dunno what the hell it would be, a Mooou perhaps?
Morphologically there's no reason why they couldn't produce offspring, but any offspring that did survive would be infertile.
BTW, you know you've been living in Alaska for too long when you start to think about crossing moose with caribou
