There are considerations to be acknowledged when shooting in the cold. but they only indirectly effect the advantage one cartridge has over another. The first consideration is priming and powder choice. The colder it gets, the more difficult it is to light the powder. The larger the case capacity and the heavier the bullet, the slower the appropriate powders tends to be, and as a rule the slower the powder the more difficult it is to ignite. In the cold, powders as a rule produce lower volumes of gas, and this reduces both pressure and velocity. It is not uncommon to load a bit hotter in the winter than you can in the summer, although I don't bother because I tend to load lots of ammo at a single sitting, so I'm never sure what time of year it might be used. In theory .223 class cartridges give up less than .308 class cartridges, which in turn give up less than Ultramag class cartridges. Despite that the performance of larger cased cartridges still outperform the smaller ones, they just give up more fps in the cold than their smaller counterparts. A word about temperature stable powders; these are designed not to produce dangerous pressures when fired at very high ambient temperatures. Temperature stability of these powders does not necessarily apply to very cold temperatures, as the purpose is to limit gas production. Hodgdon Hybrid 100V is a North American produced powder (St. Marks Powder a division of General Dynamics) is the only one that I know of that tests for low temperature stability. The extreme line of powders are Australian produced products. A total failure to fire in the cold is most likely related to the lack of maintenance or improper lubrication for the temperature the rifle is used at.
The second consideration is air density and the effect of that density on trajectory. Cold air tends to be drier than warm air because cold air cannot support as much moisture warm air. Dry air is denser than moist air, and cold air is denser than warm air. Thus at cold temperature, expect your trajectory to be steeper than in the summer just as a result of higher drag induced by denser air. A cross wind has greater effect in the cold than on a warm day, first because of the bullet's greater time of flight, so the more time wind has to work its mischief and secondly because the density of the air mass moving laterally to the bullet's flight path is higher.
The third consideration is the effect that cold has on marksmanship and rifle handling. It is not possible to have the same length of pull, eye relief and cheek weld in the cold as you have at warm temperatures unless your rifle has a fully adjustable stock. If your hands are cold, just feeling the trigger might be difficult. The technique I use it to press the side of the trigger until I can feel it, then allow my finger to slide forward until the trigger breaks. Just getting into a viable shooting position will take longer, and if you are using supported field positions, they will not be as solid due to the air pockets in the insulation of your cold weather gear.
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