The increased exploration of deeper Arctic waters motivates the designs of new floating structures to operate under harsh Arctic conditions. Based on several model tests and investigations, structures with conical sections at the waterline have been shown to be a good design for waters where drifting ice is present, because the approaching ice fails in bending, which induces smaller loads than a crushing failure of ice. However, in most Arctic waters ice features are only present during part of the year and a large portion of the operation time of these structures will be in open water. Therefore, the floating structures must perform well in both conditions.Conical sections at the waterline will induce nonlinear coupling in the hydrostatic restoring forces and moments. It is important to understand how this affects the behavior in both ice and open water conditions. In order to investigate the nonlinear coupled hydrostatic restoring forces, an exact analytic expression for the metacentric height of a regular cone is presented. This is further used to develop an exact analytic expression for the hydrostatic restoring forces and moments for any body whose waterline intersects the frustum of a cone. A platform of the shallow draft-type, the platform type for which exact hydrostatics is most important, is used as a basis for the discussion and the effect of the coupled nonlinear restoring forces is illustrated by comparison to a model test performed in both open water and ice conditions.