If you have a choice, I would recommend that you opt for a lighter weight and warmer temperature sleeping bag. You will NOT be sleeping outside.
Consider; however, that you MAY be sleeping in an inside space that is cold, relatively damp, and not properly heated. There will be enough heat to keep the pipes from freezing. Most likely, the heat will be set to keep the inside temperature at least about 5-8 degrees Celsius or more. Many albergues operate on a minimal cost basis, so providing abundant warmth to pilgrims is a luxury their business model cannot afford. They are more concerned about protecting their building and the pipes, etc.
If you are in a bedroom with multiple bunk-style beds and a door that closes, the combined warmth of the multiple bodies will raise the temperature to a point where a two or three season sleeping bag will be plenty of insulation.
Don't forget, for as often as you will need the extra insulation, you can sleep fully clothed (wearing the clean outfit you plan to walk in the next day) and wearing your fleece outer garment(s), gloves and hat. For winter pilgrimage, I recommend a watch or balaclava style microfleece stretchy cap. I did that on a few occasions even in April and May. It is part of the Camino experience.
This is another justification to increasing your budget if you can and opting to sleep in inexpensive hostals, private albergues, casa rurales, or small hotels. They usually will, at least , give you a shot of heat through the radiators in the evening and then again early in the morning. It DOES make a difference. Luxury is finding a sleeping place with heat that YOU control or enough clean blankets to layer on a bed with clean linens.
I hope this helps.