Ice nucleating particles (INPs) influence weather and climate by their effect on cloud phase state. Fatty alcohols present within aerosol particles confer a potentially important source of ice nucleation activity to sea spray aerosol produced in oceanic regions. However, their interactions with other aerosol components and the influence on freezing were previously largely unknown. Here, we report quantitative measurements of fatty alcohols in model sea spray aerosol and examine the relationships between the composition and structure of the surfactants and subphase in the context of these measurements. Deposited mixtures of surfactants retain the ability to nucleate ice, even in fatty acid-dominant compositions. Strong refreezing effects are also observed, where previously frozen water-surfactant samples nucleate more efficiently. Structural sources of refreezing behavior are identified as either kinetically trapped film states or three-dimensional (3D) solid surfactant particles. Salt effects are especially important for surfactant INPs, where high salt concentrations suppress freezing. A simple water uptake model suggests that surfactant-containing aerosol requires either very low salt content or kinetic trapping as solid particles to act as INPs in the atmosphere. These types of INPs could be identified through comparison of different INP instrument responses.