It depends on the hardener that you choose to go with. There's fast hardeners, medium, and slow. Tom21 has said 70 degrees is a good temp for epoxy to setup in though.
And you don't want to use carbon fiber or kevlar for this application. Fiberglass is the best since it has similar flexing characteristics as what your ski is made out of it. I don't know all the strength specifics on it, but I know a few layers of 1208 or 1708 will make it bombproof. Also, if you don't have much experience glassing, you don't want to start with carbon fiber or kevlar. That's a whole nother world.