The two sides of the range can actually have different weather, because the range blocks frontal movement from north to south. I have gone through the notch many times over the years and enough of those times it has been a case of going from rain to sun (or the reverse, and snow rather than rain). I have also done some overnight backpacking up there (not recently) and can tell you with certainty that what is the weather down on the flats is often quite different from what you will experience up top.
The elevated uplands of the White Mountains and the border mountains (maine-quebec border) tend to divide weather patterns into ones that migrate down the Saint Lawrence valley from weather migrating along the atlantic coast. The winds in the notches (Crawford and Franconia) and up on the tops of the peaks can be pretty strong when there is a major weather difference.
Let me warn you right here from experience: we got caught in snow up near the peaks on Memorial Day weekend one year, and it is the closest I have ever come to really being at risk of life while backpacking. It was nice down below, we hiked up into cold rain (the clouds around the mountain), and then into snow. Ended up crashing the Lake of the clouds emergency cabin. this year has not been a fast spring up this way, so even though the weather is telling us that we ought to have a beautiful weekend (FINALLY), don't count on that while up high. Go prepared. Hope for the best, prepare for the worst.
I will say that when the weather is clear, it is really something special and worth the effort. But go prepared for it to be otherwise.