The enigmatic and unexpected occurrence of coarse crystalline (gray) hematite spherules at Terra Meddiani on Mars in association with deposits of jarosite-rich sediments fueled a variety of hypotheses to explain their origin. In this study, we tested the hypothesis that freezing of aqueous hematite nanoparticle suspensions, possibly produced from low-temperature weathering of jarosite-bearing deposits, could produce coarse-grained hematite aggregate spherules. We synthesized four hematite nanoparticle suspensions with a range of sizes and morphologies and performed freezing experiments. All sizes of hematite nanoparticles rapidly aggregate during freezing. Regardless of the size or shape of the initial starting material, they rapidly collect into aggregates that are then too big to push in front of a stable advancing ice front, leading to incohesive masses of particles, rather than solid spherules. We also explored the effects of "seed" silicates, a matrix of sand grains, various concentrations of NaCl and CaCl2, and varying the freezing temperature on hematite nanoparticle aggregation. However, none of these factors resulted in mm-scale spherical aggregates. By comparing our measured freezing rates with empirical and theoretical values from the literature, we conclude that the spherules on Mars could not have been produced through the freezing of aqueous hematite nanoparticle suspensions; ice crystallization front instability disrupts the aggregation process and prevents the formation of mm-scale continuous aggregates.