During the Ice Age, hunter gatherers heavily relied on large game animals. Mammoths were probably hunted mostly for food. However, they probably used nearly every part of the animal for something....
His name is Manny.
Yes. Not only woolly mammoths, but other species, such as the Columbian mammoth (native to North America) lived during the last Ice Age.
Because they had to live in the cold or they would die because their wooly coat makes them to hot when they are in the sun.
Food & water were unavailable & frozen.