Could be rubbing on trees/fence posts. Is she itching her face at all?
If she's not: Horsecity.com | Keeping the Horse World Connected
From that link, if the horse is not itching and has facial hair loss, it could be:
1. Hair Follicle Dystrophy
2. Mange (demodectic)
4. Chronic Selenium poisoning
6. Plant toxicity (leucinosis due to ingestion of jumby tree)
7. Physiologic stress (the most common is a high fever)
9. Self trauma
10. Ringworm (~70% of the cases do not itch)
12. Grease Heel
13. Rain Rot
The link provides information on each possibility.