Hi,
I walked the route earlier this year, in a heatwave, and loved it. I did note in aulbergie books the very few winter pilgrims complaining of the cold conditions inside the aulbergies. One noted that he finally managed to rouse the (drunk) village mayor who brought six (6) logs to warm the place. Another pilgrim recorded that they draft proofed one room and took to their sleeping bags while cooking.
Outside conditions were not much better with cold and rain being frequently mentioned, but it sounds like a great challenge, if you have the proper equipment.
Enjoy
Dael