It is doable. I have not climbed the highest summit but we did climb one of the other prominent points a few years back. There were some areas that were pretty sketchy. It is like traveling through Mordor or something.

Yes, Chaos Crags is climbable to the very top. Did it several years ago in March on weekend ski in from the north west entrance. There is a steep snow slope/gully? on the north side for about a hundred or so feet, but very "doable" (you might want an axe). A nice winter alternative to Mt. Lassen with a lot less people (only saw the ranger on a ski patrol come to check out our snow cave). Enjoy!