For true cold weather, there's always a fur coat, unless fur causes the same problems that wool does.
Silk has some of the qualities of wool, and could be used for drawers, scarf, linings, etc.
A coat with a quilted silk and down lining, with a heavy cotton outside, would probably equal wool in warmth. However, I have no idea if down was used that way in the period--never thought about it before.
I'm guessing if he's allergic to wool he's also allergic to all animal fibers, mohair, cashmere, even alpaca (which I believe is not in the sheep/goat family), but knowing nothing about how wool allergies work, just thought I'd toss that idea in there.