Yes, you need a wetsuit when kayaking in the ocean. Ocean water is very cold, and the best way to prevent swim failure, cold shock, and hypothermia is by wearing a wetsuit.
A wetsuit comprises of a layer of fabric known as neoprene that is stretchy and has a semi-permeable material that allows a thin layer of water to sit between the material and your skin. This allows your skin to heat this water to your body temperature.
The warm water then forms thermal protection that shields your body against heat loss. A wetsuit is important when kayaking on cold water because it protects your body from losing heat.
You will not have fun without one. You will be too cold.