Mammoth hair, some of it long and bristly, has relatively few fibers per square inch. A mammoth's thick skin and hairy body protected it from the Arctic cold. Mammoths were larger than today's elephants. Mammoths were larger than Indian elephants, but smaller than African elephants. Usually, mammoths' tusks and heads were larger than those of all elephants.
Larger animals generate more heat per unit of their body's surface area.
Therefore, the mammoth would stay warm, even in the Arctic winter. The first sentence is true. However, an Arctic mammal must avoid having its warm skin melt snow, as explained earlier. The mammoth's skin would tend to melt snow, especially if it lay down. Its high ground pressure would have compressed and reduced the insulation provided by its hair.