Color temperature is a type that describes how "yellow" or "blue" a light's color is.
Here are some color temperature description:
2700K is considered the same color like the classic incandescent light
3000K is less bluer and is similar to halogen bulb light color, but still has a warm or bright, inviting yellow color to it.
4000K is called "neutral white" because it is neither blue nor yellow - and is the middle stage of the color temperature.
5000K is commonly used for determining color, for prints and textiles
6500K is considered natural daylight, and is a way to approximate appearance in outdoor lighting conditions
The color temperature is depend on the specific use, as your personal preference.
So after evaluation of given data we can say tha yes we can use LED high bay shop light in cold temperature as well. Color temperature will not affect by the cold or warm temperature.