Yes, you can slip, slow down on curves, watch for painted pavement, which can be extra slippery. RR tracks, too, come to think of it.
Riding in the rain is like getting in the shower with your clothes on. It just feels wrong, but no reason not to do it, either.
I have an old baseball cap that I removed the little top button and the size adjuster from, and I wear it under my helmet in the rain to help keep rain off my glasses.
You can lose some of your braking effectiveness in rain (or a lot of it, in some cases), so pay attention to brakes/pads/disks whatever to try to stay on top of things.