Native Americans used many different types of homemade traps depending upon what type of animal was being hunted. With the arrival of Europeans, spring-powered metal traps and wire loop traps became widespread as they were more efficient than the traditional styles. Traps either immobilized the animal until the hunter returned to check the trap or killed the animal outright. They would set up these traps in areas where they knew their prey would frequent and bait them with food or attractive scents. Upon trapping an animal, the would skin it and take the fur away to be stretched and cured. Once they had enough furs they would take them to a European trading post or another native settlement and exchange them for goods.
Animals trapped for the fur trade, (even those whose fur was used for felt hats like beaver) were killed and skinned. Probably preferable to being skinned alive. Beavers were generally trapped using methods that resulted in them drowning.
the heat that get into the coat stays there with trapped air
Animals in the Arctic region have white fur to camouflage them agaisnt preditors and prey. This is not because snow gets trapped in their fur, it's because they are adapted to arctic conditions. Their fur is also very thick to keep them warm.
Yes, rats have fur therefore they are furry
When it's cold, the erector pili muscles that make hair/fur stand up are active. (They're also the reason why your body hair stands when it's cold, and you get goosebumps.) The fur traps air in the spaces between individual hairs, which then act as an insulator to prevent heat loss from the body. On hot days, the cat wants to cool down so the fur lies flat to prevent any insulating air from being trapped in the fur.
They hunted and trapped animals to get the fur.
Air trapped in their fur keeps them warm
I would guess mostly for their fur.
Insulation
They trapped and traded the fur.
The animals were all trapped out and couldn't be found.
Animals trapped for the fur trade, (even those whose fur was used for felt hats like beaver) were killed and skinned. Probably preferable to being skinned alive. Beavers were generally trapped using methods that resulted in them drowning.
the heat that get into the coat stays there with trapped air
because none of the outside air can reach inside the coat and then becomes trapped inside the fur
A number of animals are valued for their fur. Around here, coyotes, fishers, mink, otter, ermine, beaver, raccoon, muskrat, and a few others are trapped and/or hunted for fur.
Air trapped in their fur keeps them warm
The earliest to go west were the fur trappers. They were following the small animals that they trapped for their pelts.