My favorite brand
(click here) actually comes in a summer and winter weight. The summer seems to have kinda loose standards, and is cheaper, but I use the winter weight which is about the equivalent on 20w oil, dyed red like tranny fluid, and seems to be fine year-round. I don't have trouble with burned bars, even slicing off stumps with old throw-away chains on a hard-nose.
I have used other brands, but I get this at the local farm store for a fairly reasonable price...the last 5 gal pail I bought was around $30 I think. Name brand oils from the Chain saw dealer might be better, but not by enough to really matter (and probably only better for the distributor), and are a lot more money.
I used to use whatever was laying around in the interest of cheap: I took home a 5 gallon pail of left-over air-compressor oil from work once. But, really, since I only use maybe 5 or 10 gallons of bar oil a year anymore, why scrimp?
When its really really cold out, like 25 below, nothing works well, and even starting a chain saw can be hard on them...plastic rewind spools get brittle, for example. I keep the saw inside if I want to be out then, and keep it in the truck cab to keep it warm until I'm ready to cut. The heat of the saw engine will keep the oil warm after that.