Wine and Faith,
Welcome to the Forum,
In the happy, easier past years
accommodation started to close mid October but some place was always open during winter. Hospitaleros usually could give advice on who/what was available on the next stage. There were no summer crowds and beds/bunks were available. I usually slept in an albergue, often the sole pilgrim, but also in back rooms of an open bar/restaurant.
Walking off-season in winter during those past years I rarely saw more than 20 pilgrims at one time. There usually was a strong sense of camaraderie amongst those on the route especially during storms or difficult stretches.
Helpful passing strangers also gave advice. Little was hectic; without the hordes of summer all had time to share info.
Nevertheless whatever the "season"
the weather can change quickly.
In March 2009 an unexpected 3 day blizzard struck Foncebadon.
Similarly November 2012 I was caught in a early white-out of snow climbing O Cebreiro.
You must be prepared whenever you walk.
See also this earlier thread re
Winter Walking
Good luck with your new plans.