My experience with the AT in CT and MA.
I hiked from Salisbury, CT to Lee, MA at the end of April. I had heavy rain, cold and sunny (with snow flurries), and warm and sunny. I took a zero at a shelter during the heavy rain.
I hiked from Lee, MA to the MA/VT border. I had one day of heavy rain, and spent half the day at a shelter. The rest of the trip was warm and sunny.
I would plan on some very wet sections, no matter what time of year you hike. The AT from Lee to Dalton passes through a beaver pond...