Two of the most socially consequential issues facing today's children are the rise of artificial intelligence (AI) and the rapid changes to the earth's climate. Both issues are complex and contested, and they are linked through the notable environmental costs of AI use. Using a systems thinking framework, we developed an interactive system called Ecoprompt to help children reason about the environmental impact of AI. EcoPrompt combines a prompt-level environmental footprint calculator with a simulation game that challenges players to reason about the impact of AI use on natural resources that the player manages. We evaluated the system through two participatory design sessions with 16 children ages 6-12. Our findings surfaced children's perspectives on societal and environmental tradeoffs of AI use, as well as their sense of agency and responsibility. Taken together, these findings suggest opportunities for broadening AI literacy to include systems-level reasoning about AI's environmental impact.