Caterpillar

There I was, happily driving along a state highway with the sun in my eye, and something tickling my leg. I reached down and found it somewhat clingy and hard to flick off. So, assuming it was an alive being, glanced down and saw a disconcertingly large fuzzy beast struggling up the the seat, attempting to get back on my leg, perhaps. Flash forward in time 30 seconds, and there I am at the nearest exit, snapping away at my relocated friend.
If anyone can ID this lovely thing I'd be so happy. I like to know the taxonomic name of the creatures I get this intimate with.