Case IH and New Holland say store the monitor in a climate-controlled environment. I would assume the other manufacturers recommend the same. The problem with LCD screens comes not so much from storing in cold weather, but actually running them in cold weather. That's when you risk damage to the display.
I also noticed this in the Ag Leader Insight manual:
"Ag Leader Technology will repair or replace at no charge any component of the INSIGHT system that fails during normal service, while being used in an approved application, within two years of the warranty start date. Warranty is not provided for damage resulting from abuse, neglect, accidents, vandalism, acts of nature, or any causes that are outside of the normal intended use of the INSIGHT system."
Depending on how Ag Leader chooses to interpret this statement, it appears to give them an out for failures caused by storage in cold weather (since this would not be a failure "during normal service, [or] while being used in an approved application"). They could also choose to call cold-weather storage "abuse [or] neglect", or say that the cold weather is an "act of nature".
Knowing Ag Leader, I think they would probably make every effort to satisfy a customer with a failed in-warranty display.