Don't scare me like that,man,i've got to go logging here forthwith!
Just kidding,Alaska(and many other very cold places) is Very well forested. Trees don't mind the cold.
Actually quite the opposite: Alaska is warming up very rapidly,which means that the underlying permafrost is melting.
As it melts the available moisture absorbs deeper,becoming less available to trees.All of Alaska's species of trees are suffering from that,the lack of moisture affects their immunity to many pests and diseases. (Warming climate was a god-sent to a number of species of bark beetles,the cold used to keep them down).
So it's actually the warming trend that is hurting Alaska's trees. Biologists agree that in about the next +/- 50 000 years Alaska will be back to the treeless savannah that it was in early Pleistocene. (i already look forward to hunting the giant sloth

).