Due to the high interest in the use of glass/epoxy laminates in aerospace applications, aviation, and as cryogenic tanks, it is crucial to understand the behavior of composites under challenging environmental conditions. Polymer composites are exposed to low temperatures, including cryogenic temperatures, which can lead to the initiation of microdamage. This paper investigates damage initiation/accumulation and its influence on the properties of cross-ply woven glass fiber epoxy composites at low temperatures compared to room temperature conditions. To evaluate the influence of a low-temperature environment on the mechanical performance of glass fiber reinforced epoxy composite (GFRP) laminates, three types of test campaigns were carried out: quasi-static tensile tests and stepwise increasing loading/unloading cyclic tensile tests at room temperature and in a low-temperature environment (−50 °C). We demonstrated that the initial stiffness of the laminates increased at low temperatures. On the other hand, there were no observed changes in the type or mechanism of developed damage in the two test conditions. However, the reduction in stiffness due to the accumulated damage was more significant for the laminates tested at low temperatures (~17% vs. ~11%). Exceptions were noted in a few formulations where the extent of damage at low temperatures was insignificant (<1%) compared to that at room temperature. Since some of the studied laminates exhibited a relatively minor decrease in stiffness (~2–3%), we can also conclude that the formulation of matrix material plays an important role in delaying the initiation and formation of damage.