Doing accurate temperature measurements at low temperatures is not really different from “normal” situations when it is warm outdoors.
Real measurement problems mainly occur when moving the camera from a warm to a cold environment or vice versa, as the operation condition then changes, especially when doing this rapidly. Unstable environmental temperature will cause more temperature drift and give problems to the detector response. So if you move the camera from a warm car to the outside and back in, this might cause some problems. But if the camera continuously is at the same (cold) temperature, you don't have this issue.
Considering you still are targeting objects hotter than the environment, only delta T to the environmental temperature gets higher, which actually is rather an advantage.
What you have to do is simply to adjust reflected apparent temperature (Trefl) to the correct level. Being outdoors, this most probably is the tricky part, but not because of the atmospheric temperature. Trefl outdoors depends more on the current situation of the sky (clear, cloudy, sun, no sun). Also be aware of the angle of the reflections – is it the sky, the ground, some buildings, a forest being the source of reflection?