Differential pair impedance vs temperature
I would not suspect the impedance was changing but rather the quality of your interconnect + the components on the -55C rated wifi card and whatever is at the other end result in failure. There is no doubt that timing inside the chips will change as temperature goes down.  If you have built yourself (or bought yourself) a link (your motherboard).  That works at room temperature, the design may not be good enough that combined it works at -55C. I would demand my vendor help read the BER out of their WiFi chip and monitor it as temperature drops.  

If you can't get that it would be interesting to look at how the eye changes with a scope (you can keep probe body out of the oven if you're creative.

If you really believe your impedance is changing, and I suspect it is not, you could rent a TDR or a VNA and measure it at different temperatures.

Oh! Another good thing you could try if you can't get any help from the vendor. You could rent the gear to do PCIe compliance testing. There you can definitely put the devices in different modes and generate traffic and see how it responds.  The lecroy PERT comes to mind as a good piece of test gear.

Despite how wide spread it is PCIe is still a fickle beast.  Oh and it would be worth looking to see if they have passed PCIe compliance (and if they had to play any tricks to do so).

One last piece of advice.  If you're running at PCIe 3.0 try to force it to 1.0 and see if it's better.  If you're running x4 or x8, try to force it to x1 (either with a piece of kapton tape or your bios).