If it isn't possible to find santa on a frozen moon or planet due to lack of critters that would be able to drag the sleigh. What if Santa lived on a "sunny" moon where there are suitable critters for dragging a fully loaded sleigh? If that is the case there are some prime targets that I would like to share:
The Ursadak is a critter that was taken into the swarm and evolved to the mighty ultralisk. The females are not as aggreisve as the males counterparts and the lack dangerous horns. I could envision a friendly pack of Ursadak's girls pulling the sleigh forward. They would endure the long travel distances but if only Blizzard would take back the Ultralisk charge upgrade so that lore miners could trace back the charge ability to the Ursadak hunting behavior. It could an answer to explain how the heavyweights could take off and fly away.
The Karak is my second example as a potential candidate as it's neck could serve the same purpose as that of a horse. In other sci-fi worlds similar creatures have been domesticated. A kindred species is the Tauntaun, a biped too, in the star wars universe and is seen and used by Luke Skywalker in Empire Strikes Back. The Karak is quite populous as it exits on several worlds and of course on the home homeworld Shakuras but has not been seen on a frozen ice world (yet)?
I could for one imagine a santa claus type figure commanding a couple of Karak's although their obedience is untested a worthy candidate they are.
Have I missed any worlds or locations? On a more general note it's sad to see so few domesticated animals in the starcraft universe something that the starwars universe certainly didn't lack.