From someone who used to do a lot of hill walking. Make sure you are wearing decent waterproof clothing, preferably a breathable fabric, as otherwise you can get just as wet from perspiration if you are not careful. The dryer you can keep, the more comfortable you'll feel.

Something I've noticed from playing in the rain is, that even supposedly wet weather golf gloves get soaked through. So a spare dry glove to use, for when the rain finally abates, is a good move.

Yeah, fully agree with the contact lens point. nothing worse than glasses covered in rain drops, though glasses do have the added advantage of keeping the wind off bare eyes.

Give yourself plenty of time to play the game. make the most of a wet day. Don't simply keep slogging along, just because you feel you need to get round as quick as possible. Give yourself time to stand & enjoy nature in the rain. After all you've come out to enjoy yourself. Have a flask of hot coffee, half way around. a little nip of something warming as the season gets colder & wetter is never a bad idea.

And again time related, there is nothing better than enjoying a warm meal while you dry off properly. I shall certainly be making full use of the clubhouse as the weather gets progressively more inclement.