Actually, I think Underhill was the first woman to climb the NH4K in winter, as she suggests in her book, Give Me The Hills:
"This game was an offshoot, of course, of that very popular game of the Appalachian Mountain Club, Climbing the Four-thousanders, which was set in motion, and such vigorous and enthusiastic motion, in 1958. Our game —'ours' because we were the first to play it— followed right along. As the initiators we set the rules, which concerned the definition of 'winter'. 'Snow on the ground' and other namby-pamby criteria definitely did not count. 'Winter' was to be measured exclusively by the calendar. In 1960, for instance, winter began at 3:27 PM on Wednesday, December 21, too late to get up to Crag Camp by daylight."
So, I don't know whether that makes her the first woman to climb NH4Ks and/or the first in winter. I'll look it up when I get home to the book. Underhill went on to do other "lists" after that.
Julie Boardman's When Women and Mountains Meet includes Underhill as well as some other White Mountain "first" women: the Austin sisters, who were the first women to climb Mount Washington, and Laura Waterman, Natalie Davis, and Debbie O'Neill, the first women who traversed the Presidentials in winter.