Hi Jake. My area isn't all that severe for weather. Caribou opens August 1st; it's often quite warm during the days in August (for here anyway - 60s, maybe low 70s), Even later in season, into September, freezing's usually not an issue, though it can get down into the 30s at night. I don't anticipate weather being a factor. Both caribou and moose die pretty easy, once hit. I have zero concerns about a crossbow's effect on a caribou. I believe, based on what I've read, that if I take and pass the state course, I'm good to go. The area I live in... there's no special seasons for different weapons, though we do have seasons that are area residents only, which is pretty sweet for those of us who live here.
Hope you get to scratch your itch, regarding AK. Moving here a long time ago was one of the best decisions I ever made.