Yes, I ride in the rain, mostly because sitting around in the rain can be pretty boring. I might take cover from time to time when there's a lot of lightening or hail, or when the rain is so hard I can't see where I'm going, but cover is not always available.
As to how I cope, it depends a lot on the temperature. If you tour in the summer, a lot of the time it's okay to just get wet. But if it's cold, I might start adding rain gear. If you're climbing or otherwise working hard, you will likely still get wet even with rain gear on. There's not much you can do about that. Pick your poison.
I don't consider rain covers for my shoes worth the weight and trouble. But I do take waterproof socks. Of course my feet still get wet from the sweat, but somehow it feels better to me.