The mosquito-borne disease dengue is a growing global health concern, with ongoing efforts to develop early warning systems to predict outbreaks and support early intervention efforts. Such systems typically integrate climate data since dengue is climate-sensitive (e.g., seasonal peaks in dengue cases follow the monsoon rains), but specific pathways by which climate impacts dengue are poorly elucidated. We investigate one such pathway: climate impacts on dengue-transmitting mosquitoes via breeding habitats. We use a specialized mathematical model to simulate development and survival of the temperature-sensitive mosquito eggs, larvae, and pupae within an aquatic container breeding habitat (e.g., a water-filled bucket). We tested this model using weather data records for three Sri Lankan cities, finding promising similarities between simulated mosquito population size and historical dengue cases. We also tested this model using weather forecasts, assessing whether the benefit of advance notice provided by weather forecasts outweighs their inherent inaccuracies. We found that weather forecast-based simulations perform similarly to weather record-based simulations for one city, while accuracy suffers elsewhere due to weather forecast data errors. However, these errors might be minimized with further work, suggesting that with continued development the modeling pipeline may provide valuable input for dengue risk prediction using weather forecasts.