Yuck - rain and cold, never a good time.
BUT over the years I have found that moose will remain active during the rain - especially during this time of year. It always seemed to me that the only thing slowing down their activity during the pre-rut/rut is HOT weather. So long as it' s not hot, I' d say you stand a chance at seeing some good movement.
And with the woods being wet it' ll make it all that much easier for you to sneak up on a big bull and get a shot.