Funny you should mention umbrellas. This summer on a back country rescue we had a victim of a horse wreck laying out in the trail in the hot sun for probably 30 minutes. We didn't want to move her to the shade until the back board and c-collar arrived. A group of off-roaders showed up with 2 umbrellas and provided shade for the addtional 30 minute wait. It was a godsend. I have been carrying one in my truck ever since.

I also carry an empty backpack for the reasons already stated by others. I have the room for a full size external frame pack. A walk home in winter will require more bulky gear than my SAR pack can hold.
leo