With the number of post and pictures of successful hunts in Canada I have started planning, or perhaps just dreaming, of a caribou hunt in either Canada or Alaska. Which ever path I take there would be the issue, if it is an issue, of either transporting game through Canada from Alaska or from Canada into US. Is this an issue?

Yes, but not nearly as big an issue as the handgun you will want to take with you to Alaska-through Canada-that is an issue!    

You are completely legal to bring back your game meat with you.  Once you have taken an animal, the outfitter will provide you with the necessary paperwork to transport the meat and hide.  If you plan on flying beware because it is unbelievably cost prohibitive to ship back any meat via the plane.  If you are driving it is obviously not an issue.  We hauled a trailer with chest freezer on it and small generator to newfoundland from ohio when we went for moose.  We are going up again in 2015.  After last years fiasco with the TSA and flying into canada and the customs people we have made the decision to drive to wherever we are going to hunt if at all possible.  We left our bear meat with the natives in Alberta because it was so expensive to bring it home. I think I paid something like 110.00 just to carry the hide and head back on the plane.  Make sure that you realize that when you start looking at hunts the actual hunt price is really just the start of the expenses.  You can usually figure close to double that by the time you get done paying for everything. Good luck and good hunting