Hi, Marcelo,
I have spent several one-year stints in Portugal over the past decade, and though the weather is unpredictable, it's pretty safe to say that the temperatures in January are of a different magnitude from what you would experience in northern Europe. In Lisbon, for instance, even in deepest winter, the temperatures usually hit at least 13 or 14 celsius. The northern interior can of course get colder, but the real cold in Portugal is reserved for the mountains in the Serra da Estrela and maybe some other areas around Braganca, so you should be ok.
If you look through some of the other posts in both the Vdlp section and the Camino Portugues section of this forum, you'll see some discussions about accommodation that may be of interest to you. In Portugal, at least south of Porto, there is only limited pilgrim accommodation, though that is changing. North of porto and in Spain, you'll find many more albergues but I assume that in January you will frequently have to resort to a "residencial" or "pensao", but in Portugal I found that the cost was usually under 20 or 25 euros a night. On the Vdlp, there are a lot more albergues, but I don't know about opening in the winter time. And you can expect private accommodation in Spain to be more expensive than in Portugal.
You should look at the
http://www.vialusitana.org website, because it has a lot of good information about the Caminho Portugues, and it's all in Portuguese! The members of that organization are very helpful and dedicated peregrinos, as well. Bom caminho, Laurie