Formal:
* Drapery
* Hangings
* Valance
* Panel
* Screen
Informal:
* Covering
* Shade
* Blind
* Window treatment
* Fabric
Specific types:
* Sheer
* Voile
* Lace
* Velvet
* Brocade
* Damask
* Tulle
Literary:
* Veil
* Mantle
* Shroud
* Drape
The best word to use will depend on the specific situation and the desired tone.