A broadband dielectric spectroscopy study was conducted on a partially crystallized 10 wt% poly(N-isopropylacrylamide) [PNIPAM] microgel aqueous suspension to investigate the dielectric relaxation of ice in microgel suspensions. The measurements covered a frequency range of 10 mHz to 10 MHz and at temperatures ranging from 123 K to 273 K. Two distinct relaxation processes were observed at specific frequencies below the melting temperature. One is associated with the combination of the local chain motion of PNIPAM and interfacial polarization in the uncrystallized phase, while another is associated with ice. To understand the temperature-dependent behaviour of the ice relaxation process, the relaxation time of ice was compared with those observed in other frozen polymer water mixtures, including gelatin, poly-vinylpyrrolidone (PVP), and bovine serum albumin (BSA). For concentrations ≥ 10 wt%, the temperature dependence of the relaxation time of ice was found to be independent. Therefore, the study primarily focused on the 10 wt% data for easier comprehension of the ice relaxation process. It was found that the microgel and globular protein BSA had no significant effect on ice crystallization, while gelatin slowed down the crystallization process, and PVP accelerated it. To discuss the mechanism of the dielectric relaxation of ice, the trap-controlled proton transport model developed by Khamzin et al. [Chem. Phys., 2021, 541, 111040.] was employed. The model was used to discuss the dynamic heterogeneity of ice observed in this investigation, distinguishing it from the spatial heterogeneity of ice commonly discussed.