I have also had the tourist pat problem, my reasponse if someone just walks up and starts petting without my permission etc, is usually to smile sweetly and back my horse away, explaining that shes not safe for strangers. (She is safe, but its the only excuse that works for me)
Of course, if anyone comes up to me and asks politely if they may pat my horse, I will dismount, and show them where and how she likes her pats.
Its kinda funny tho, because Shakira has learnt to associate tourists with praise and a rest, so as we canter down the beach her ears will flick to any person who walks past, wondering if they want to say hello. Shes too polite to stop or nicker, however.