Dan Bern has a nice song he wrote in Alaska, "Alaska Highway". It's more a free running riff on the road, but the locals always like hearing him do it.

More trad. numbers are:
perhaps the greatest of the US State songs, "The Alaska Flag" which begins: "Eight stars of gold on a field of blue
Alaska's flag, may it mean to you
The blue of the sea, the evening sky the mountain lakes and the flow'rs nearby"

A good more traditional song may be: "The 30 US on the wall"

There's the song about the frozen logger: "my lover was a logger, there's none like him today, why if you'd pour syrup on it, he would eat a bale of hay..."

Stan Rogers had a great country western tune about a Northern trucker who gets permanent case of cabin fever in "Canol Road". This is more BC/ Yukon Territory stuff but it counts IMNSHO in that it involves the cold, alcohol, violence, and a bad ending. Too Tres Alaskan.

If you have access to the net, buy the CDs advertized by "Mr. Whitekeys" of the Fly By Night CLub. They do a wonderful performance set in a sleazy Spenard joint which captures Alaska better'n most.

There's a lot of homegrown bluegrass and folk as well.

good luck.