In normal weather, I use a little Gunslick oil, or Hoppes 9 with rust protection...
In cold weather, I use LSA:
www.sarcoinc.com/new60.htmlUS Military gun oil that is supposedly designed to withstand extreme temperatures. I've used it last winter with no malfunctions in my AR (even firing cheap-ass barnaul russian ammo). Seems to work fine for me in ~10 degree weather from last january's shoot. Haven't tried shooting subzero with my AR15 yet.
Camping in the cold weather is one thing... I can build a fire, setup camp, and enjoy a peaceful clear winter night out in rural MN. A truly humbling and peaceful thing.
Anyway, I don't go out shooting a lot in the winter anymore (haven't had much time on my hands these days). I did a few years back, but that was just with bolt action 22's... Nothing that really "Jams". But my extremely limited experience with LSA seems to work fine.