The Qinghai–Tibet Plateau is the main permafrost area in China. Concrete structures constructed on permafrost are affected by the early negative-temperature environment. In particular, the negative-temperature environment seriously affects the strength growth process and the frost resistance of concrete (FRC). Therefore, this study considered the influence of the gas content, water–binder ratio (w/b), age, and other factors on the strength variation law and FRC under −3 °C curing conditions. Nuclear magnetic resonance (NMR) was used to analyze the pore structure of concrete before and after freeze–thaw cycles (FTCs). The results showed that the compressive strength of the concrete (CSC) under −3 °C curing was only 57.8–86.4% of that cured under standard conditions. The CSC under −3 °C curing showed an obvious age-lag phenomenon. The FRC under −3 °C curing was much lower than that under standard curing. The porosity of the concrete under −3 °C curing was greater, with a higher percentage of harmful and multi-harmful pores than that under standard curing. The concrete properties deteriorated primarily because curing at −3 °C hindered the hydration reaction compared with standard methods. This hindrance resulted in diminished hydration development, weakening the concrete’s structural integrity. Under both curing conditions, when the gas content was between 3.2% and 3.8%, the frost resistance was the best. This is because a gas content within this range effectively enhances the internal pore structure, therefore relieving the swelling pressure caused by FTCs. Based on the freeze–thaw damage (FTD) model proposed by previous authors, a new model for the CSC under −3 °C curing reaching that of the concrete under standard curing for 28 d was established in this study. This advanced model was capable of accurately assessing the FTD of concrete structures in permafrost regions. Finally, the life expectancy of concrete in Northwest China was predicted. The life of the concrete reached 46.9 years under standard curing, while the longest life of the concrete under −3 °C curing was only 12.9 years. Therefore, attention should be paid to constructing and curing concrete structures in cold environments.