Ice nucleation is an important process in numerous environmental systems such as atmospheric aerosol droplets or biological tissues. Here we analyze two widely used approaches for describing homogeneous ice nucleation in aqueous solutions with respect to their applicability to heterogeneous ice nucleation processes: the lambda approach and the water-activity-based approach. We study experimentally the heterogeneous ice nucleation behaviour of mineral dust particles and biological ice nuclei (Snomax; Pseudomonas syringae) in aqueous solutions as a function of solute concentration for various solutes (sulfuric acid, ammonium sulfate, glucose, and poly(ethylene glycol) with two different molar masses of 400 and 6000 g mol(-1)). We show that the ice nucleation temperature and the corresponding lambda values depend on both the type of ice nucleus and the type of solute, while the water-activity-based approach depends only on the type of ice nucleus when the solution water activity is known. Finally, we employ both approaches to the study of ice nucleation in biological systems such as the supercooling point of living larvae and insects. We show that the behaviour of freeze tolerant and freeze avoiding species can be described using the two approaches and we discuss how the analysis can be used to interpret experimental results of the freezing behaviour of living species.