I was out cutting last weekend, with temps 22 - 28F during the day. I was running a Stihl 064, a Husqvarna T435, and an Echo 510EVL, all started with a full tank of standard bar oil. I noticed they had varying degrees of success in keeping the bar lubed, but all ran dryer than normal. I also noticed my bar oil was so thick in the bottle, it almost could not be poured. After I was able to use some of the oil in each saw, I replaced with Winter Grade, and things flowed a little better.
I'm sold on Winter Grade (gotta run something, might as well be the right stuff for the conditions), but have also used 5W-30 in the past, when it was too cold to pour my standard bar oil.
I was switching saws a good bit (T435 for clearing branches, 064 for the big trunks, 510EVL for everything else), so none had a chance to get all that warm.