As long as you don't put your umbrella up inside the cockpit (that brings bad luck, amongst other things!) and you can still see where you are going and the ground, it shouldn't cause too much of a problem. Where I used to fly it was unusual to have a day when you could fly for 10 mins without rain!!
The bigger thing to look out for when there is rain is the type of cloud that it causing it. If it is a large CB, then steer well clear as the turbulence even at several miles from the cloud, is likely to be quite intense - not to mention the possibility of lightning strikes....... "I told you not to mention those!"