I'm leaning a bit towards owner (or customer ) because it better describes the relationship between the partner and the cart.  When fulfilling sales orders it often happens that several partners will be involved with the process (eg. sales clerk, quality control officer, order picking guy, ...).  If it is required to keep track of them they should be stored in a collection of partners associated to an order.   For a cart it isn't really needed at this point and just the owner / customer of the cart should be sufficient.  The cleanest way to combine both approaches is to have one "default" owner partner field and later on define an optional collection if you want to store more partners.