Software-as-a-Service solutions are increasingly being adopted when developing software applications, as they are scalable, cost-effective, and facilitate rapid deployment while providing high availability and flexibility. However, the impact of Software-as-a-Service in terms of carbon emissions is not yet adequately addressed as a design concern, and most of the existing efforts revolve around measuring and containing the carbon impact after the deployment. Our work proposes a model-driven reasoning framework that integrates UML-based software architecture modeling with carbon-aware concerns. Architectural elements are supplemented with sustainability and performance properties of interest through a dedicated Domain Specific Language; then, a model-driven transformation generates a simulation model to evaluate multiple architectural designs according to their Software Carbon Intensity and performance metrics. The results guide decision-making by assessing and comparing the trade-offs between performance and carbon intensity for the analyzed designs. In this way, the reasoning framework provides an automated, tool-supported approach to designing environmentally responsible Software-as-a-Service applications.