I don't have a very strong background in physics and electrical engineering but just from knowing that the major or basically all energy consumption of a processor comes from switching its transistors and from the the electrical resistance, which is very high I would say as a processor is basically a very thigh cable at very low voltages and very high currents, and that the resistance and hence the wasted heat is lower at lower temperatures, I would conclude, that a processor in a cooler environment also consumes less energy.
This also leads to another other question: assuming that a CPU has a specific power consumption at a specific level of utilisation, would the power consumption be much more than twice as high at "double" utilisation (although this is hard to define in practice) as the overall temperature would increase and the same "work" would lead to more energy loss due to more resistance?
To give a short background on the question: I was wondering if my notebook battery life lasts longer if I'm using it outside in the winter for example. Of course this is hard to answer as there are many other factors like the behaviour of the battery itself at different temperatures and the display, but this has lead to the basic question described above.