Under fierce market competition and the demand for low-carbon economy, cold chain logistics companies have to pay attention to customer satisfaction and carbon emissions for better development. In order to simultaneously consider cost, customer satisfaction, and carbon emissions in the cold chain logistics path optimization problem, based on the idea of cost–benefit, this paper proposes a comprehensive cold chain vehicle routing problem optimization model with the objective function of minimizing the cost of unit satisfied customer. For customer satisfaction, this paper uses the punctuality of delivery as the evaluation standard. For carbon emissions, this paper introduces the carbon trading mechanism to calculate carbon emissions costs. An actual case data is used with a cycle evolutionary genetic algorithm to carry out computational experiments in the model. First, the effectiveness of the algorithm and model were verified by a numerical comparison experiment. The optimization results of the model show that increasing the total cost by a small amount can greatly improve average customer satisfaction, thereby obtaining a highly cost-effective solution. Second, the impact of carbon price on total costs, carbon emissions, and average customer satisfaction have also been numerically analyzed. The experimental results show that as carbon price increases, there are two opposite trends in total costs, depending on whether carbon quota is sufficient. Increasing carbon price within a certain range can effectively reduce carbon emissions, but at the same time it will reduce average customer satisfaction to a certain extent; there is a trade-off between carbon emissions and customer satisfaction. This model enriches the optimization research of cold chain logistics distribution, and the study results complement the impact research of carbon price on carbon emissions and customer satisfaction. Finally, some practical managerial implications for enterprises and government are offered.