The dear paint we used to have not only took off his masks, I think he buried them–never found most of them. On him and on an earlier “redhead” chestnut with pink nose, I used a “show gloss” sunscreen–can’t remember the name, came in a white plastic tub with a silvery-blue label (I’ll see if I can find it)–and it worked beautifully preventing sunburn, even though it was clear gloss. It had no odor, so they didn’t tend to mind it.
I agree with whoever suggested trying a no-ears mask. My yearling removed her with-ears mask daily, and finally also apparently buried it (still missing!) She’s now using a no-ears version, and has only taken it off once.