Adds Hardness to the Bar?: Most definitely! Even at small amounts (5-10%), adds hardness to the final bar.
Creates Fluffy Lather?: Nope...
In fact, too much of any of the butters will really kill fluffy lather.
Creates Stable Lather?: Yes...the lather is low and creamy and stable.
Adds Moisturizing Qualities?: Most definitely! Cocoa butter, and all of the nut butters are GREAT providers of skin-loving qualities in your soap. Very moisturizing in soaps or just straight out of the jar.
Other Qualities?: Cocoa butter, even though it's more expensive than other base oils, is one of the staples in my basic soap recipe. Even at 5% or so, it imparts lovely moisturizing and helps create a nice hard bar. Natural cocoa butter has a yummy warm chocolate scent that will come through in balms and lotions, and even comes through in soap if you use enough in the recipe and don't mask it with a strong fragrance oil. The deodorized/refined cocoa butter has much less scent.
