The sea ice interaction with a structure may cause system changes and affect the feasibility of common approaches to track modal parameters. In this paper, a covariance-driven stochastic subspace identification method is used to identify the natural frequencies from 190 time series of ice actions against a lighthouse structure. The results are sorted into groups defined by the observed ice conditions and governing ice failure mechanisms during the ice-structure interaction. The identified natural frequencies vary substantially within each individual group and between the groups. Recordings with flexural failures and a north-south ice-drift direction consistently rendered the same identified frequencies, whereas crushing seemed to create large amounts of variability in the identified frequencies. The results show the need for more high-fidelity data to assess whether modern system identification methods can be used to monitor system changes and support decision-making for operations of structures in ice-infested waters, such as offshore wind structures.