Honestly, if you TREASURE your original DVDs and CDs make copies of them and then leave the copies in the trailer or vehicle.
Pressed (as in store bought) DVDs and CDs typically do not degrade data wise however they DO get brittle in a critical area, the CENTER of the disc.
If the disc cracks for any reason in the center area the player will not be able get a firm grip on the disc and often the disc doesn't play or if it plays will skip or freeze.
Burned copies have the same issue as pressed when it comes to the center but also have the additional issue of heat and UV fading of the dye layer and over time can become unreliable. But the best part of this is if you have your original disc you simply make another CHEAP copy.
BOTH pressed and burned DVDs and CDs CAN be damaged via scratches and or haze on the data surface.
Its your money to spend so if you want to leave say 50 DVDs (or CDs)for a value of $750 laying around with large temperature changes and or the possibility of theft that is your choice.
I don't.
Yes, I have kept CDs in a vehicle for short times, several weeks but I cycled them through playing them a couple of times then exchanging them with other discs. This reduces the time spent in extreme temps and allowed me to enjoy my collection while driving.
Now days however I have stereos which play MP3 files from USB drives, I rip my music to the USB drives and no longer have CDs in my vehicle.
You can do the same thing with DVDs, rip them to video files, then use a portable media player (these are standalone players which play many different audio and video file types). These players can have internal HDs and or play from USB drives. Non HD media players can be had for as low as $30, HD Media players can be has for as low as $60.
If I was wanting to leave my collection in a trailer I would go with the media player route or at least make backup copies of the original discs.