The weather could be just about anything. Most likely days would be in the 70s, but could be higher. Nights could be in the 40s-50s, but below freezing is not unknown. I once climbed Big Slide the weekend before Memorial Day. It rained heavily in the Keene valley the night before the hike, but at the summits there was about 2-3 inches of new snow (which fell on bare ground). I also passed though a section of ice covered trees just below reaching the elevations with snow. It was beautiful, and posed no problem hiking in summer boots. Expect mud on the trails, and prepare for the biting black flies.