List looks fine to me, for winter camping.
I'd also say bring less shirts, pullovers, gloves... unlike on a wilderness hike, there's lots of opportunity to wash/dry clothes.
When you camp in albergue gardens, or stay in an albergue from time to time, you can wash and dry there. But then again, you've apparently walked long distances with that setup and it works. So why not.
Inflatable+foam mat is wise in winter.
With regards to camping on the Camino, you probably won't get many encouraging replies, because most of the forum members do not camp and do not want to camp. It's rare for pilgrims to sleep in tents, but some do.
I've camped along the Francés because I love sleeping outdoors, and would bring a tent again. That was in summer, though, when campsites were open. I do not wild camp, and therefore didn't camp every night (I love the albergues, too, and there wasn't a legal campsite every night).
There were a few albergues that allowed tents in their garden (for a fee, of course!) and there are also some official campsites, but those are most likely closed in the winter.
When you get the opportunity to camp in an albergue garden, that's nice because you can take a shower, wash clothes, use the kitchen ect., meet pilgrims, but you still have your tent as your own little home. Sadly most albergues do not allow camping even if you offer the same fee as for a bed, but it is worth a try.
Roncesvalles for example allowed me to camp, and the albergue Padres Reparadores in Puente la Reina.
Wild camping is not legal in many parts of Spain and usually not tolerated by locals either. It is probably still possible if you're good at stealth camping, but I certainly wouldn't recommend it. Heard many stories from people who were woken up at night by police and had to take down their tent. Sleeping outdoors without a tent seems to be tolerated better, as long as there's no fire or littering involved (which for a respectful tent camping hiker should be normal, anyway). As a guest in the country I wouldn't want to break rules or annoy the locals.
So, camping along the Camino is possible, but complicated. You might end up in the albergues more often than you can imagine now!
Buen camping Camino, from a fellow tent pilgrim!
(picture in front of the albergue in Roncesvalles)
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