Artificial spin ices (ASIs) are magnetic metamaterials comprising geometrically tiled strongly-interacting nanomagnets. There is significant interest in these systems spanning the fundamental physics of many-body systems to potential applications in neuromorphic computation, logic, and recently reconfigurable magnonics. Magnonics focused studies on ASI have to date have focused on the in-field GHz spin-wave response, convoluting effects from applied field, nanofabrication imperfections ('quenched disorder') and microstate-dependent dipolar field landscapes. Here, we investigate zero-field measurements of the spin-wave response and demonstrate its ability to provide a 'spectral fingerprint' of the system microstate. Removing applied field allows deconvolution of distinct contributions to reversal dynamics from the spin-wave spectra, directly measuring dipolar field strength and quenched disorder as well as net magnetisation. We demonstrate the efficacy and sensitivity of this approach by measuring ASI in three microstates with identical (zero) magnetisation, indistinguishable via magnetometry. The zero-field spin-wave response provides distinct spectral fingerprints of each state, allowing rapid, scaleable microstate readout. As artificial spin systems progress toward device implementation, zero-field functionality is crucial to minimize the power consumption associated with electromagnets. Several proposed hardware neuromorphic computation schemes hinge on leveraging dynamic measurement of ASI microstates to perform computation for which spectral fingerprinting provides a potential solution.