You can buy cotton nose flaps that attach to the halter - He is already wearing a halter so it should be no big deal.
I have two white faced chestnuts. One has really bad sun sensitivity that started with a reaction to a plant and has never gone away - He has no hair on his pink nose at all.
Normal sunscreen never worked for him. You need a zinc cream, you can use regular white people zinc but I like Filta-Bac which also has antiseptic properties. I have recently veered away from this though as he got a habit of wiping it off on the nearest horse, which made me very unpopular at shows!
I recently found a powdered sunscreen called mypony, it's great, except because he has no hair on his nose it doesn't stick very well. It's great on my mare though, stays on all day, looks natural, and they don't mind it going on.
But basically the only way I manage it fully in the paddock with with some kind of nose cover. He wipes sunscreen off on his legs throughout the day. I use either the cotton nose flap that threads on to a halter, or a nose screen from nag horse ranch (These guys are great!).