I'm just guessing but I'd bet the .44 mag is the most popular round and most likely a Ruger Super Black Hawk, maybe some Smiths. Probably a few carry a 357 but aren't planning on slowing down moose very quickly.
Since you pose the question, it occurred to me that part of the race runs thru the Farewell area where there are bison. But I've never heard that bison were a problem.
I think the official Iditarod site might have a place you could ask such questions and get a more informed answer than mine.
I don't know if mushers are required to carry a gun.
HTH