I'm sure a cold wet climate would hurt such items. And the advancement of teamwork and other ingenuity would result in different forms of hunting.
Doesn't do a whole lot of good for flintlock firearms either.
Now I’m not up on the nuances of early frontier combat, but that doesn’t make much sense to me. Aren’t early firearms also susceptible to wet weather? Sure there are some things that can be done to seal things up to keep power dry, and most of the sinew bowstrings I have seen were treated in one way or another to make them more or less, waterproof. Also water doesn’t really destroy sinew it makes it flexible and stretchy, but bowstrings were generally pre-stretched. In either case, it doesn’t seem like the means of dealing with wet weather are foolproof, so it doesn’t seem like it would change the odds all that much. By the time waterproof cartridges came out the indians were using firearms as well and it wasn’t uncommon for Indians to have more advanced guns than the infantry (though I’m sure the Army faced groups of Indians with a wide range of armaments).
As far as the Inuit are concerned I know they had to get to sophisticated lengths to make bows from materials that could be obtained in the far north. The cable backed bow is the first type that comes to mind. I imagine at some point before these clever designs were invented bows would have been a great disadvantage to far north hunters. Another interesting tidbit I learned about the arctic and subarctic tribes from the explorer Samuel Hearne’s journal “A Journey to the Northern Ocean” is that they traded so extensively amongst themselves that they frequently managed to obtain guns before ever meeting a European. However, if you were in a tribe was disliked by tribes who had made contact with the fur trade then you were in trouble.