Outside all winter?? I'd get a Wipperman stainless steel chain, then oil it with whatever wet lube is least expensive at your local department store or bike shop and re-apply often.
I saw some people mention chain-l. Might lubricate chains well but I won't use it, it causes way, way too much mess.
I use Dupont wax lube and I throw away my chains every 1500-1700 miles. I'm heavy and I stand on the pedals a lot, result is chain stretch. I find the cheap chains actually last me longer because they're not trying to take all sorts of material out to make them lighter, like for example with the drilled side plates and hollow pins you see on some chains. I'm using KMC 9SL on my bikes and I get them online for $13.
I once ran a high zoot chain for like 5000 miles on Prolink lube, cleaning it religiously, but it snapped one day and not only that it caused a ton of wear on my expensive Campy casette, so much so that both had to be replaced. Now, I do none of those things, i.e., buy high end chains, high end casettes or run chains that long. I find cheap chains replaced often lead to long cassette and chainring life and better shifting to boot. Plus the wax lube doesn't attract dirt. The downside is of course you have to re-apply every 200ish miles. I don't mind, doesn't take that long when your chain stays clean all the time!
But uh yeah for OP - get a stainless chain and wet lube.