My advice - Man up
My Brother digs graves 6 days a week, 52 weeks a year. He also goes in on a Sunday morning to make sure the bins are empty for the visitors to graves. If you wear lots of thin layers then it shouldn't be an issue.
We used to have to work in very cold theatres doing transplants. Some of the operations went on for 11hrs plus and we only wore thin cotton scrubs.
If they thought it was a safety issue then I'm sure they'd reschedule it. They have a duty of care after all.
If you have any concerns about the safety and roadworthiness of the vehicles, then it's your responsibility to voice them. It's not only putting your life at risk, but also those of the public.