[Sashimister]

Thanks for the replies. Here are the readings and meanings.

雨男（あめおとこ）
A man/boy who claims to bring rain to wherever he goes. These are regular dudes, not shamans, mind you. Just goes to show how much we like talking about the weather.

雪男（ゆきおとこ）
A yeti.

晴れ女（はれおんな）
steven above explained the term perfectly.

So, I obviously included 雪男 to make the question trickier and more fun. Use these words actively and surprise your Japanese friends! Naturally, we also say 晴れ男 and 雨女 as well. Also, remember to willingly talk about the weather if you want to please us.
_______

KyleGoetz brought up バックシャーン. (In recent years, it's more often written and read バックシャン.)

This is an unusual word in that it's a mixture of English ("back") and German ("schon") yet it's probably used only in Japanese. It means a person (esp. a woman) who looks much better from the back than the front.