For butane/isobutane/propane canisters, the stove design, affecting the temperature in the canister or liquid feed pipe, and the boiling point of the gas mixture would matter. At very low temperatures even the O ring rubber type would matter as some types go less rubbery and do not seal properly.
For instance, if the temperature of an upright butane canister drops below -0.5C/43F at sea level and one bar pressure, then the butane no longer boils/evaporates in the canister and the gas flow stops. There needs to be enough heat from a warmer place (air outside, ground or stove flame radiation) to supply energy to drive enough evaporation for cooking.
Isopropane has a lower boiling point and propane a lower one yet; the temperature where a particular canister becomes impractical under normal use depends on the gas mixture.
(Lower outside pressure will help a bit as the boiling point would be lower, but typically at such altitude the temperature is also lower!)
A more robust winter gas canister stove solution would be one where
a) The canister is turned upside down so the existing gas in the canister drives liquid fuel out of it, ie. you need very little heat directed to the canister.
b) There is a heated supply pipe or heat shunt from the flame to where the fuel enters the burner, which ensures enough energy is supplied to evaporate the fuel before it reaches the burner head once the stove is started.
The latter is an important safety consideration as liquid butane etc. reaching the burner would mean a lot of gas suddenly supplied to the burner as the flame evaporates it, ie. a flare-up. So upside down canisters are best used with stoves designed for that!
Those features (which are unusual) should allow you to use a gas canister stove with a good mixture at -25C or a bit lower at sea level according to Backpacking Light (note only first page is subscription free).
So it may be colder on the top of Everest, depending on the time, but would you be there in that case? :)