Just a couple of thoughts from a non-expert.

When people still used the old-style wood-and-rawhide showshoes, it was standard practice to put a couple of coats of exterior grade varnish on both the wood and the leather at the start of each season. This would keep everything tight, light, and dry. Until it was abraded off by snow.

Alternatively, I suppose you could soak the handle with liquid silicone (the kind used to re-waterproof tent flies etc.). Penetrating, inexpensive, and likely quite effective.

My 2c.