I build a roofing top piece and place it on top of my gates to prevent them from rotting. All roofing parts are immune to rain. I was unaware that the angled wood parts seem to be immune (probably a bug), but everything else made of wood should be susceptible.

Nothing rots to below 50% health, so generally it doesn't matter aside from gates which need HP to keep enemies out.

Iron gates and gratings seem to be immune to rain also.