I made a conical rice hat for Skyrim yesterday. But since I still cannot manage to get anything to work in that game, I decided to make it for Oblivion instead. I named it Sakkat because Ragnarok Online had a similar hat with that name and I think it's better than "Conical Rice Hat". It is on right ring slot, so you keep your hair when wearing it. Depending of your hair style, they might go through as seen in the image below. I fitted the hat to be fitted on Head06 head because I think this is one of the most used one. The strap may look a bit loose on different head such a Ren's.
I added 4 of them in a bag in Testinghall.
You can download it here: Sakkat.7z