When compared how the light is generated, carbon arc is in fact an incandescen light source. And because it operates at such high temperature, the 45degC change (caused when the ambient goes from zero to the -45) makes not that much difference there, compare to all other effects. But at such cold temperatures I would suspect the mechanical electrode adjustment system the carbon arc needs will have some problems operating correctly.
Andfor the others: Ignoring the potential ballast problems (mainly electronic - electrolytic capacitors will have very high ESR, component parameter shifts may be so severe the circuit my not be working at all; talking about temperatures below the designed minimum) the lower the operating temperature, more effect the cold ambient would have. The thing is, hotter the lamp operates, the more itbwould be sensitive to power changes, so needs some form of temperature stabilization mechanism. And this mechanism then covers for the ambient temperature as well. Most dominant mechanism in practically all high temperature sources is the thermal radiation (power proportional to (absolute temperature)^4), which becomes stronger at higher temperatures. So no wonder the worst are the fluorescent (inherently sensitive, but mainly folow the ambient), followed by LPS and the best are then the incandescent sources (inherenly sensitive too, but very strong temperature stabilization by the radiation). The LEDs may have even better efficacy (that alone would make them better than the best), but their color will shift (that is a performance degradation).
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