Shower etiquette: Onsen (japanese public baths)

How to produce shower thoughts ?

Rate my routine :

1. Shower but no soap, just wet the body
2. Remove dripping water from body with the small towel
3. Wet small towel with cold water and remove excess water from the towel
4. Go to sauna for 12 mins using cold towel
5. Rince the sweat off from body and towel in shower
6. Cold water bath
7. Wash full body and head
8. Hot water bath
9. Wash full body and head
10. Dry with towel
11. Exit bath area and change back.