100326-0831 EST
The National Semiconductor GFCI chip is used in the Leviton and has an operating temperature range of -40 to +70 deg C. The Cooper probably uses the same chip. These would come from different manufacturing batches. Thus, unlikely this basic element would be the problem.
There are other components in the GFCI that might have temperature problems, but unlikely at the low temperature end vs high temperature. Generally leakage resistance goes down as temperature goes up, and this is the wrong direction to cause problems.
The internal test resistor in GFCIs is 15,000 ohms. This produces 8 MA at 120 V. If the sensitivity of the GFCI increased as temperature decreased, then you would need to be experimenting with test leakage resistance above 15,000 ohms. 5 MA at 120 is 24,000 ohms (use a 22 k or 27 k), 2.5 MA at 120 is 48,000 (use a 47 k), 100k would produce 1.2 MA. 1/2 W resistors would be OK for momentary use.
It might be worth while to take several of the GFCIs that had caused problems and put them in a freezer and run load and leakage current tests. It is true that load current should have virtually no effect on the GFCI. But under sever temperature conditions one can not rule out some strange effect. This is why my neighbor, before retirement chief engineer of Ford light truck chassis, insisted on real world field tests under actual environment conditions. He would not depend on on laboratory tests alone. This was especially true on seals.
You have a different latching mechanism in the Leviton and Cooper GFCIs, and therefore that area is an unlikely cause.
When it gets cold again and the problem reoccurs, then take a hair dryer and heat the GFCI, and see if this corrects the problem. If it does, then investigation of GFCI problems should be considered. If not, then somewhere after the GFCI is the problem.
I like the ideas of moisture, and or problems in the load presented in the previous posts.
If you have available CO2. a suitable valve, a small orifice, and a siphon tank or turn a standard tank upside-down, then you can generate a very low temperature for testing the the GFCIs in place.
Easier maybe, but harder to control temperature, is packing dry ice around the box. You do not want to cool the GFCI too much.
With liquid CO2 you can get down to -73 deg C.
http://en.wikipedia.org/wiki/Dry_ice
http://www.associatedenvironmental-bma.com/models/bd.asp
http://www.electrotechsystems.com/getManual.asp?DocID=92
.