Most fur hats run $200 to $600 depending on the types of fur used and how much additional sewing is needed.
For a hat out of your own fur you will have some barter room if you trade the fur remains to the maker. However, a summer pelt is going to make for poor winter hat material. The fur will have to be fleshed and tanned as well so that adds to the total cost.
Boundary Fur Sewing in Fairbanks might abe able to answer some questions about having a hat made from your own fur.
http://www.boundaryfursewing.com/p/about-bfs.html
Dahlberg's Taxidermy in Palmer (see their Facebook page) will flesh and tan a hide and then have a fur sewing friend of theirs make throw pillows from that hide. They have examples of moose and caribou covered pillows on their FB page. I don't know if their fur sewing friend does hats. I'll have to check on that.
The below link will make your wallet and credit card scream, but how cool will you look in that hat?
http://www.alaskrafts.com/fl-hats4-wolf.htm
Or you can get in touch with Bushrat on the AOD. Real Deal bush dwelling trapper made fur products.
http://forums.outdoorsdirectory.com/...-pieces-and-hat-pics
Also from the AOD with lots of local contact info
http://forums.outdoorsdirectory.com/...-for-a-fur-hat-maker
The person that does the pillows. I would go with a full fur hat total mountain man style.
http://alaskaspiritcrafts.com/