Sure they would. The area that would support them would just be shifting. So what a mammoth needs? -- food -- no predators that kills them all (remember, it'

Sure they would. The area that would support them would just be shifting. So what a mammoth needs? -- food -- no predators that kills them all (remember, it's humans that killed it) -- not too hot climate. Does it require actual ice? Of course not. It is unlikely it lived on ice, it still needed to eat something and that means most likely tundra of some kind. There is still a lot of tundra today available.