I have never experienced temperatures below -25*F, so I can't comment on behavior at -50*F.
About 15 years ago, while on a winter camping trip I noticed that output of my incan MiniMags really dropped off when the temperature got much below 20*F.
On the next trip out, with the forecast calling for a low of 0*F, I brought along a MiniMag, Mag 2C and Mag 2D all incans loaded with fresh cells. The MiniMag performed similar to the previous trip, leading me to believe that AA size alkalines were of limited use in cold weather. I was surprised that the C cell light performed about like the MiniMag and was only good for about 10*F use. The Mag 2D was the clear winner, with only a modest drop in light output at 0*F.
Thinking back on my tests today, and now knowing that human perception of light is on a logarithmic scale, the output of the 2D light had probably dropped much more than I realized.
Today, the AA lithiums are the clear stand out in cold weather performance with a -60*F rating. If I recall correctly, CR123s are rated for use down to -20*F but have been reported to have adequate performance at lower temperatures.
With the advent of LEDs I have started using smaller lights, which carry easily in my pockets, so I haven't really noticed cold related issues. Then again, the smaller lights are loaded with AA lithiums and/or CR123s.
I'm now curious as to how a MiniMag LED, loaded with today's improved alkaline cells, would perform in the cold.