We had the same problem with my daughter's new filly - the problem was that the filly came to us 80% wild and developed sores under the gunk.
In the end, because I couldn't get ner her with clippers and using sissors was too dangerous - did I mention mostly wild? - we used Veet human hair removal stuff. It was a pain in the rear and left a huge bald spot on her girth area as well as some chemical burns, but it worked. It took a week for the chemical burns to fade with treatment, but now she is fine - just has a bit bald spot.
If clippers are an option, I would use clippers - though by all means try oil and the other topical ointments above, if they work, it is better than bald spots in winter!
So, I guess all I can offer is a long distance horse like hug....