If the ear is 'crusty' inside that is usally a sign of ear mites being in there. If applying olive oil, use at body temperature, apply liberally onto cotton wool and wipe all of inside of ear gently. Don't use the same cotton pad for both ears, use a fresh one for each. If it's bad get the vet out, one trip should do it.
If it was me, I'd give the mare her favourite treat at the same time if poss, so she associates having her ears 'oiled' with a treat, as she will need it doing a few times.