Hi Bill. Yes, once you get to temperatures around freezing you have to use thinner chain oil to protect bar and chain. Up here you can buy the lighter grade, might be available in your area with some searching. I use varsol or "paint thinner" (not laquer thinner)! to achieve the same effect. Just don't use too much. I guess it helps if you know the proper consistency of winter bar oil. I suspect ATF may be a good thinner. I would be cautious about vegetable oil, as it tends to "freeze" at sub zero temperatures. Personally I would avoid diesel, probably just as good, but has a persistent smell.
The aim is to provide an oil which will freely lubricate the bar and chain. You can check this by revving the saw over wood or snow, it has to always cast a bit of visible oil. Any time this isn't the case damage is likely. First be sure the oiler port is clear, and the bar port, and the chain groove in the bar is scraped clean (I keep a flattened finish nail as a cleaning tool, clean and reverse the bar with every chain change, as soon as the chain begins to feel dull). If necessary you may have to adjust the oiler, the goal being to lubricate, but always have a bit of oil left when a tank of fuel has run out.
If using winter oil, be careful to change it back in the spring.
As for winter cutting, I actually think wood cuts best in cold weather, cuts cleaner.