Obamacare killed them off?
They certainly could have migrated.
Caribou do so today, over distances that would be comparable, and they also deal with permafrost, taiga and tundra.
Elephants are known to travel such distances also. And they are not a bit slow-moving in fact. I don’t see why mammoths have to be assumed to move slowly.
They could also, like other still existent arctic animals, have dealt with ice ages by simply displacing their range southwards. That sort of thing is well documented in the fossil record. Since it is also well documented that the earth has been through numerous ice age cycles, obviously the mammoths survived several of these.
I think the best explanation for why they disappeared is that people showed up, and the Mammoths proved to be easy prey.