Nimh rechargeables can get flakey sometimes, due to diff factors, their age, how they are charged, the charger, if they have been charged after fully discharge or not etc, or simply cuz they are getting to the end of their cycle life. Years using these for photo use has shown me this, and I have experienced sudden drops like you say, but not due to temps, just because they are getting flakey. Cold temp changes do not "make" batteries do weird stuff, cold temps make batteries perform less, a good battery will lose power over time as it cools, but a bad battery can and will do weird sudden drops like yoiu describe, the cold in your case is just a factor in bringing the battery down in charge.
Ive seen laptop batteries do this as well-again, not cold related, but they can show a full charge and then go down out of the blue.
Pro camera batteries do this also, so when batteries start doing this, they should be marked as suspect and get new rechargeables. New ones that are properly charged will not do be affected like you describe, in fact a good battery is just going to hold a charge longer in the cold than a suspect one, just as a new alkaline battery will hold a charge inthe cold longer than a weak alkaline.

re chargers, to make your nimh batteries last longer, the use of a charger that takes longer to charge and put less heat into the battery as it charges (1 hr ones are the worst in this regard) will result in your batteries lasting longer, and performing better over their life.
Youcould also have one or more of the nimh's in your group in your light that are flakey , this can cause weird behaviour too when 1 or 2 of 4 go down quickly.

your theory of leaving a battery in the cold doesnt make sense, a battery always has more charge at warmer temps, so you are always better off with it being warmer to begin with, it means it will hold whatever charge it can for longer. If it starts out at -5c all day before use, its already at a disadvantage compared to a room temp battery that will gradually cool down with exposure to cold temps.