The surface mixed layer (ML) governs atmosphere-ocean fluxes, and thereby affects Earth's climate. Accurate representation of ML processes in ocean models remains a challenge, however. The O(100) m deep ML exhibits substantial horizontal thermohaline gradients, despite being near-homogenous vertically, making it an ideal location for processes that result from the nonlinearity of the equation of state, such as cabbeling and thermobaricity. Traditional approaches to investigate these processes focus on their roles in interior water-mass transformation and are ill suited to examine their influence on the ML. However, given the climatic significance of the ML, quantifying the extent to which cabbeling and thermobaricity influence the ML density field offers insight into improving ML representations in ocean models. A recent simplified equation of state of seawater allows the local effects of cabbeling and thermobaric processes in the ML to be expressed analytically as functions of the local temperature gradient and ML depth. These simplified expressions are used to estimate the extent to which cabbeling and thermobaricity contribute to local ML density differences. These estimates compare well with values calculated directly using the complete nonlinear equation of state. Cabbeling and thermobaricity predominantly influence the ML density field poleward of 30 degrees. Mixed layer thermobaricity is basin-scale and winter intensified, while ML cabbeling is perennial and localized to intense, zonally coherent regions associated with strong temperature fronts, such as the Antarctic Circumpolar Current and the Kuroshio and Gulf Stream Extensions. For latitudes between 40 degrees and 50 degrees in both hemispheres, the zonally averaged effects of ML cabbeling and ML thermobaricity can contribute on the order of 10% of the local ML density difference.