We investigate the accessibility and projected low-noise performance of single-soliton Kerr frequency combs in silicon nitride microresonators enabled by operating at cryogenic temperatures as low as 7 K. The resulting 2-orders-of-magnitude reduction in the thermorefractive coefficient relative to room temperature enables direct access to single bright Kerr soliton states through adiabatic frequency tuning of the pump laser while remaining in thermal equilibrium. Our experimental results, supported by theoretical modeling, show that single solitons are easily accessible at temperatures below 60 K for the microresonator device under study. We further demonstrate that the cryogenic temperature primarily impacts the thermorefractive coefficient. Other parameters critical to the generation of solitons, such as quality factor, dispersion, and effective nonlinearity, are unaltered. Finally, we discuss the potential improvement in thermorefractive noise resulting from cryogenic operation. The results of this study open up new directions in advancing chip-scale frequency-comb optical clocks and metrology at cryogenic temperatures.