I moved from CA to LA in the heat of the summer which was just the opposite weather that you are exepcting. Here's what I did:
bag snakes and box them in rubbermades. duct tape them shut.
I only like to bag monitors. Other lizards need a suitably sized rubbermade or deli cup with appropriate substrate. The substrate can be shavings, newspaper, moss etc.. but give them plenty of it. I mean lots of it. This will help them feel safe and reduce stress while baffling them against sudden jolts. It also helps insulate against cold and provide humidity when appropriate.
Use deli cups or small sealable containers for spiders.
Don't drive straight thru. Stop and spend the night in a hotel. Bring your animals in the room with you and check on them. If you have any soiled substrate, you can deal with it easier than on the side of the road. BRING EXTRA SUBSTRATE AND DUCT TAPE. You may also want to mist them or give them a drink from a bowl.
Also, if you have the room (if you don't, then try to make room) put them in the seating area of the car with you where you have the temp controlled. Avoid car trunks and truck beds. It's cold out there not to mention the dangers of carbon monoxide. Watch out for excessive temps on the floor boards, but also keep in mind that it's warmth can be a benfit.
Safe travels,
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Zoodude
"Just because I'm paranoid, it doesn't mean they aren't after me."