I still don't know how to deal with light on a rainy day like today...
I turn my camera off and work around the house to make my better half happy. Haha.
Seriously though, it is a problem for all cameras. You can raise the ISO or try to get as close as possible. Noise in High ISO is unavoidable. Some use Topaz Lab software to denoise; but that also takes away some details. One good thing about cloudy day is that you don't have to worry about high contrast between light and shadow. As long as you don't point your camera high towards grey sky you should get some nice results in a cloudy day.