Neil, I am assuming this work is exterior? If it is going to be cold over the next few days and you decide to hold off for the rain to pass and the warmer weather to return. Be sure to cover the area with some form of water barrier. The last thing you want to do is wait for a week or two, for the wood to dry. You will still get some moisture in the wood but least it will not be drenched from the rain.
I tend to agree with Karl as far as using some Japan in your primer. Although it may not be completely dry, it will at least be at a soft stage where the exterior of the paint will dry enough to keep the moisture out.
If you are able to get a small coat on early enough in the day it may setup just enough to dry.
BTW- I am a former resident of Good Ole NH.. I sure do miss the snow.. not to mention the ocean. Nothing like driving down old rt1- coastal route through Rye on into Hampton.