A penis that is cold, but still hard. It causes the middle to become shriveled and small, but the blood flow stays in the head, causing a normal erection, which makes the penis the shape of an hourglass.
Jill: Holy crap! What's wrong with your dick?
John: Nothing. Just have a case of hourglass penis.
Jill: I've never seen anything like it!
John: What do you mean. It's cold, so I have a half-boner. I mean come on! Your blowing me on a ski lift!