Background: Respiratory viral infections (RVIs) exhibit seasonal patterns influenced by biological, ecological, and climatic factors. Weather variables such as temperature, humidity, and wind impact the transmission of droplet-borne viruses, potentially affecting disease severity. However, the role of climate in predicting complications in pediatric RVIs remains unclear, particularly in the context of climate-change-driven extreme weather events. Methods: This retrospective cohort study analyzed 1610 hospitalization records of children (0–18 years) with lower respiratory tract infections in Rome, Italy, between 2018 and 2023. Viral pathogens were identified using nasopharyngeal molecular testing, and weather data from the week preceding hospitalization were collected. Several machine learning models were tested, including logistic regression and random forest, comparing the baseline (demographic and clinical) models with those including climate variables. Results: Logistic regression showed a slight improvement in predicting severe RVIs with the inclusion of weather variables, with accuracy increasing from 0.785 to 0.793. Average temperature, dew point, and humidity emerged as significant contributors. Other algorithms did not demonstrate similar improvements. Conclusions: Climate variables can enhance logistic regression models’ ability to predict RVI severity, but their inconsistent impact across algorithms highlights challenges in integrating environmental data into clinical predictions. Further research is needed to refine these models for use in reliable healthcare applications.