In a pinch you can do what this young women did on a very wet start in the morning-- improvise. They were a tough couple. They were riding the Icefield Parkway in Alberta, Canada from Jasper to Banff and back to Jasper during a long weekend. It was cold and the guy rode in shorts. We were camping near each other during a cold wet night.
We met them on their return trip two days later, and I noticed the guy was wearing a new looking pair of long-underwear under his shorts.
My wife in her wet weather gear on that cold rainy day: helmet cover, rain jacket, rain pants and gloves. In a pinch, we will use plastic bags, but usually good wool socks work well for us.