For Monadnock, white dot is definitely the most traveled so I’d recommend that. I’ve done it a dozen or more times in winter and microspikes have always been more than sufficient. Even with a foot of snow I’ve also not seen it need snowshoes yet. Other trails there the conditions vary a lot more, even white cross needs crampons at times.
There hasn’t been a lot of precipitation up there this winter, either, so there’s a lot of bare rock still. I’m going again tomorrow so I’ll see how this week’s snow has changed things.