Are dogs' noses physically sensitive?

Whenever I accidentally brush against my dog's nose or touch it while trying to pet his face, he turns his face in annoyance. This happens when I touch any part of his nose - the top, front, or sides. I've never noticed this before, but I was wondering if this is a trait in most dogs. I'm also concerned that he might have injured his nose. I have a Jack Russell Terrier, and he chases everything that moves. A problem is that he slides across my floors in attempt to stop and seldom crashes into the walls. Is this something I should get checked by the Vet? Or is this normal? Any feedback is highly appreciated. Thanks.