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)
3. Hypothyroidism
4. Chronic Selenium poisoning
5. Iodism
6. Plant toxicity (leucinosis due to ingestion of jumby tree)
7. Physiologic stress (the most common is a high fever)
8. Anhidrosis
9. Self trauma
10. Ringworm (~70% of the cases do not itch)
11. Photosensitization
12. Grease Heel
13. Rain Rot
The link provides information on each possibility.