Impact of rain on hikes?

My partner and I are traveling to WM from Texas and we've already booked the rental car, hotel, and Cog train. We're planning on driving the highway and doing the waterfall hikes along the way.

But I've been seeing reports about the potential nor'easter. Although Northern New Hampshire won't be impacted as much, there's still a huge chance of rain.

Should we just cancel and get a refund while we still can? Should I ere on the safer side and not hike in the rain? Will the rain be not much of an issue on the trails? Any advice is appreciated!