Howdy Frank,
Your question as to low temperatures for sawchain has at least three answers:
chains made with .50Cr, .70Ni have a designed critical temperature of minus 35F below zero. All the older professional chains were made this way. Carlton and Stihl still are. Oregon, I'm not so sure of anymore. These chains will have reasonable resistance to crack formations from frictionally altered part bottom surfaces.
chains made with .25Cr and .30Ni should be expected to have a critical temperature around minus 20F below zero. Chain's in this group will have notably less resistance to frictionaly altered surface crack growth to failure.
The third class of chains is the consumer chains with .01Cr and .01Ni. These have a critical operating temperature around zero F, and next to no resistance to propogation of frictionally formed and thermal fatigue cracks. These chains are definitly not wise to use in cold weather.
In all cases, the use of a good light motor oil for chain and bar lube will decrease the part bottom failures in cold weather. John is right about the plunge into snow. That means the chain gets hot on the bar and then is quenched in the snow. Many cycles of this, and the material forms a whole series of micro cracks on the sidelink part bottoms, first at the heel (back rivet) of the cutters. Nickle in the alloy slows the growth of these cracks. These are called thermal fatigue cracks for the above reason.
A good professional chain, used in -20 to -30F weather and in full time professional use, will usually have a useful life of two weeks if good oil is used and enough of it to have a visible sling off of the bar nose when not cutting. The HP of the saw makes little difference. (The speed does! Overly lowering depthgauges will cause premature failure).
Regards,
Walt Galer