One of the more common questions people ask is why they don't seem more moose hide clothing items around. It's a fair question: moose are large animals with lots of fur, so surely some of that is useful. And even many people who grew up knowing not to use moose fur for anything serious don't know why they shouldn't use it. It's a simple enough answer, though: the hair sheds like crazy. The hair shafts are constantly breaking and shedding over time, meaning very quickly you'll lose some of your best guard hairs, and be left with little warmth. You can tan moose hide, but the only thing I've ever seen it used for is the de-haired leather.
The reason moose hair sheds so much is that the hairs themselves, like hair of all deer, are hollow. They almost look like someone's blown bubbles into the middle of the shaft. I'd love to post a picture of it right here, but I don't have one that I have rights to. But I can link to this picture here on another website. That beautifully shows the inside of a red deer (aka, elk) hair shaft. Most deer (including Caribou, moose, and so on) have hollow hair; most thinking is that this is a trait to help them thermoregulate, or maintain a consistent body temperature. The hollow shafts provide additional dead air space to keep a pocket of air warmed (or cooled) to their body temperature. I haven't seen this idea rigorously tested, though.