If you consider the trunk of a car a trailer like environment I think you'd be just fine with a couple of precautions. Not sure what your idea of cold is, but up here in Canada -40 is quite common in the winter and in the summer +40 C (probably +60 C in the trunk of the car). I use a dcx2496 and multiple power amps and processing for my car audio and not once in 23 years has the cold ever given me greif on the electronics or displays (summer heat and the amps is another story, they work fine until they overheat then cut out until they cool down enough to kick in again, no permanent damage). The dcx, amps, and processors power up every single time i start my car even with 1/8" frost completely covering the displays and cases. No issues on the electronics ever. However, like was mentioned, condensation could form when said electronics are brought into a warm humid environment. Usually in the winter the heated venues won't be that humid anyways, we've never had a problem with that up here in Canada ever.
Twice I've had issues with speakers affected by the cold if driven hard without time to warm up. Once I've had a glue failure between the spider and the basket in -40 when the speaker was driven hard without time to warm up. It was a dynaudio 6.5" midbass
. The other time was when I brought in 2 JBL SRX715's in from -40 and ran pink noise through them at extremely high volume levels (by accident, damm faders) without time for them to warm up. The titamium compression driver diaphrams turned into confetti literally. The biggest piece of titamium in one piece was smaller than a hole punch. JBL service department said that was only the second time ever that they seen that. They wouldn't cover it under warrantee
