If someone has norovirus and pets/cuddles with a dog, is there a chance the virus germs can stay on the dogs fur and be contagious if i pet the dog?

Dog fomites-unlikely: This is what is called a 'fomite' which probably means nothing to you, but the dog is an object which could harbor and then transmit these germs -IN THEORY. Mostly, norovirus attacks cruise ships, where someone who's had diarrhea, opens a door, and the door knob gets these viruses on it. That person who held the dog hopefully cleaned up after a diarrheal BM and didn't contaminate it. Wash the dog!