The Camino Portuguese from Oporto north, and any camino in Galicia will be rainy in December, with the Portuguese or Ingles being the rainiest. The
Camino Frances in Castile and Leon is cooler but noticeably drier. (Dealing with cool temperatures is much easier than dealing with rain. Just layer carefully.)
In a nutshell, in December the Portuguese (using Vigo and Santiago as a reference) experiences 15 or 16 days or rain a month, and a total of about 260 mm/10" of rain. Leon and Burgos average about 9 days of rain, totaling about 60 mm/2.5". The early part of Galicia (e.g., Sarria, using values for Lugo) falls in the middle, 14 days of rain totaling about 135 mm/5.5". If you want to compare detailed statistics, the Spanish meteorology service has simple tables you can use to compare by place and month of the year.
http://www.aemet.es/es/serviciosclimaticos/datosclimatologicos/valoresclimatologicos
June-mid-September is the relatively dry period on the Camino Portuguese. My wife and I walked in early October and got socked with heavy rain seven of nine days. Our shoes never dried, and smelled so horrible that we threw them out at the end. I also walked from Burgos to Villafranco del Bierzo (just before the Leon-Galicia border) in December and had only one day of steady rain. (If it snows, there is almost always a nearby small road alternative to follow if you are wearing sneakers or just want to be drier.)
Most private albergues on the Frances close in December, but enough municipal and religious ones and hostales and hotels stay open to manage the walk without a problem. (Every fall a list of albergues that will be open gets posted on this site.) There are enough hotels and casas rurais on the Portugues to walk in December too, if you don't mind paying for them.
My notes on walking in December:
https://www.caminodesantiago.me/community/threads/short-winter-camino-notes.30363/
Enjoy it! I would love to be going.