I've always used the low tech approach when I had to video in the rain and simply used a large trash bag over the camera/VF and cut an opening for the snout of the lens and another for the 5" studio viewfinder. It keeps the camera dry and functional even in a downpour. It works as well or better than the custom raincoats for cameras and I can buy a heck of a lot of trash bags for the cost of one of those. Of course the OPERATOR doesn't get that benefit but they generally don't short out when they get wet. Short temper maybe, but not short out.

I'd use much the same approach with a DSLR... probably using a ziplock bag instead of a trash bag. Stuff the camera into the bag, tear a hole to poke the lens hood out of and reach into the open end of the bag to operate the camera. That should keep it dry and functional; the only issue would be the optical viewfinder... you could use a transparent bag and see through that. I would certainly use a UV filter; you will get drops on the front element and a filter's easier & safer to clean.