For a sturdy bandage that doesn't slip or stick to the horse, there are several bandage options available.
Things to Consider:
Vetrap -- This product is an excellent choice for a bandage that only sticks to itself, stretches nicely, and stays cool. It will also not absorb moisture, keeping your horse dry.
Wrap Loose -- Make sure that your wrapping is secure, yet not too tight, which can cut off circulation or damage tendons.
Stock up -- Be sure to have plenty of bandages on hand so that you're ready for any accidents and first aid incidents that may arise.