I've hiked in the rain wearing shorts, gaiters and a Goretex parka or light rain jacket. I've also worn a wool pullover instead of a jacket in light rain. This used to be common in New Zealand before the advent of the newer fabrics. I'm sure some people still wear wool.

We were usually going from hut to hut, so there was plenty of space to dry out wet clothes and the huts were fairly warm-some of them have wood stoves in them.

I don't remember getting too warm, but the weather there is cool or cold most of the time, so not really an issue.