Biological tissues decay over time after harvesting, which alters their biomechanical properties. This poses logistical challenges for studies investigating passive arterial biomechanics as tissues need to be characterized shortly after excision. Freezing and cryopreservation methods can help alleviate the need for biomechanical testing of fresh tissue in human ex vivo studies. However, these methods tend to eliminate or reduce arterial cell functionality and affect passive biomechanics. Furthermore, their impact on dynamic arterial biomechanics remains unknown despite arterial viscoelastic properties being an integral component contributing to arterial stiffness under in vivo loading conditions. The present study aims to investigate the impact of rapid cooling and subsequent storage at −80 °C on the passive viscoelastic properties of arterial tissue and aid in ascertaining whether this is a suitable method to delay tissue analysis for studies investigating passive arterial biomechanics. Control and frozen abdominal rat aorta segments were quasi-statically and dynamically tested using a biaxial testing set-up. The results were modeled using a constituent-based quasi-linear viscoelastic modeling framework, yielding directional stiffness parameters, individual constituent biomechanical contributions, and a quantification of viscoelastic stiffening under dynamic pressurization conditions. Frozen samples displayed significantly decreased wall thickness, viscoelastic dissipation, viscoelastic stiffening, and significantly decreased circumferential deformation with changes in luminal pressure. Furthermore, frozen samples displayed significantly increased circumferential stiffness, pulse wave velocity, and collagen load bearing. Consequently, these changes should be considered when utilizing this tissue preservation method to delay biomechanical characterization of rat aortic tissue.