warts are more common in young horses and just disappear on their own. We had an instructor who messed about putting sudocrem on our youngster and just managed to spread them around! I would check with the vet that they are just warts as a precaution though.
Ditto what fruitloop says, though 8 yrs isn't that young any more. My horse had a previous 2-stage vetting certificate the dealer had done when we bought her which mentioned warts on her nose, but by the time we had a 5-stage vetting a few months later, they weren't there any more. She was rising 5 at that time. The insurers still insisted on putting warts on her policy as an exclusion (typically).
If they don't go of their own accord, you might try Dermafas which got rid of ear plaques in my horse, it is one of those all purpose miracle creams like Camrosa, which is another one you could consider.
My horse had warts on his nose a few years ago at this time of year, he was about 17/18, we just left them and they disappeared by themselves by september time
My mare had warts on her nose when she was 4. They looked like little cauliflower florets!! I had the vet check them out and he said they would go away by themselves, and sure enough, they did and without any treatment. They were odd looking though!