Don't let a little rain stop you from getting in your morning run. If you use rain for an excuse today you'll find another excuse tomorrow and pretty soon you'll be in a rut. Cover your head and keep your feet dry and you'll be all set.
I remember when I was in the SMB when it was raining in East Lansing we would yell "It's snowing in Ann Arbor". The rain only increased our intensity. I apply that to my runs today. It may be raining, but somewhere else it is worse. The fact that I get out and do it despite the rain only fulfills my self gratification that much more. That's why we do it in the first place right? It's going to be a great day!!!