Big Flaw
Ok so I know this is animation (cartoon) and as such disbelief should be suspended - but suspended how far?
Scientifically this film is ludicrous, mixing two distinctly different geological time zones and creatures into one all encompasing umbrella labelled "Ice Age"
The Ice Age as most scientist define it is a period known as the Pleistocene - the last 2 million years of history up to 10,000 years ago when it changed to the Holocene.
Smilodon (Sabre Tooth Tigers) were primarilly Mesozoic creatures that became extinct along with the rest of the dinosaurs at the end of the Cretaceous.
Woolly mammoth - Mammuthus primigenius (Blumenbach, 1799), were primarilly Pleistocene creatures. And yes they were around at the same time as humans.
Yada yada - can't have an extinct creature roaming around in a later time frame.
And as for sloths being around where there was permafrost - again dubious.