I've had spiders in my car wing mirrors for all of the two years I've had the car. I regularly use a car wash. I've also jet washed the car a number of times (after leaving it near a lime tree) The spiders always weave new webs overnight following the washes. They seem to be active and living quite happily.
I have one too. If, when I'm about to set off, I see him on the outside of the mirror, I touch him gently and he runs back inside, behind the glass. I don't want the poor thing to be blasted off the mirror when the air starts whizzing past him. Soft eh?