Running in the rain isn't that bad. Once you've started, you get used to it pretty quickly.
You're probably going to have a shower when you get home anyway, and the shower feels so much nicer if you're coming in from the cold.
The only trouble is that before you start, you need to persuade yourself that this is true. Looking out of the window, the rain seems like an insurmountable obstacle - you couldn't possibly go out there in that weather. In reality, though, it's just another excuse to not run.