Cooling assemblies having a sealable cooling chamber formed as the interior volume of a curved or spherical outer container and a sealable inner canister are disclosed. The outer container may be provided as a multi-layer container having an external elastomeric shell. The external elastomeric shell may have an inner framework including a plurality of longitudinal ribs and a reinforcing wall. A movable flap adjustable between a projecting condition in which the flap extends from the exterior surface of the outer container and a closed position in which the flap doesn't project may be provided for supporting the cooling assembly in a stationary condition and the flap may be used as a handle for opening a lid.