According to Google Image Seach :) more than a half has body, and some have a hat
http://www.google.com.ar/search?hl=en&q=moai&gs_sm=e...
(IIRC, all most of them had had a hut, but in most of them the hat had fallen an been lost.)
(IIRC, all most of them had had a hut, but in most of them the hat had fallen an been lost.)
[1] http://static.tvtropes.org/pmwiki/pub/images/Moai_Heads.png