too Cold, never!
Too cold for camping out, doing a long hike, lots of exposure? Maybe & yes & depending on your health, this is a big concern for some.
This type of cold shrinks the margin of error. (In summer you can do lots of silly things - leave coat at home, little food, no matches, etc & likely get away with it if you get lost, just a cool night out)
If you're fit & have no health issues (or even suspect it) trips under 8 miles RT not too far from safety shouldn't be an issue.
Tecumseh, Lonesome Lake, Cannon, Wildcat by Ski slopes, the floor of Tucks (avoiding avy prone areas depending on conditions) some of the peaks from Highland Center should be okay too.
You’ll want to make any early start & do something pretty easy when you know you’ll be back to the car well before dark.
Most of us here (probably not all though) know that trails in winter don’t really look like the summer trails as far as navigation goes. It’s even harder finding your way back after dark.
It’s not likely going to be a good weekend for a Pemi-Traverse, a Presidential Traverse & it’s not really a smart weekend for an Owl’s Head trip or Carrigain.