If you happen to have a cycling vest, and a microweight or lightweight long-sleeve wool shirt, wear those two in combination.

Your arms will get a little wet, but will stay warm, because the wool won't lose much warmth when wet.

And you'll be able to breathe. (I've yet to have a jacket that breathes well biking - in ANY weather.)

I like the idea that someone posted here, of carrying an extra pair of socks and an extra pair of gloves. Those two items seem to be the weak spots when riding in the rain.

Mariposa