Mount Washington sits at the end of a long, wide east-west running valley, in an area with predominantly western winds. This gives the wind an unusually long "fetch" to build strength over.

That, combined with the orographic lift as the air flows over the mountain, leads to unusually strong winds.

Apparently three major air streams pass right over the northeast, and it's the highest point (by a fair margin) east of the Mississippi. So it essentially gets a direct "hit" of speedy air that's been uninterrupted for thousands of miles, from multiple angles.

Exposure. There are 75mph+ winds at the top pretty much constantly and it’s the highest point around especially facing northwest