Nowadays climate change is affecting the planet’s biodiversity, and livestock practices must adapt themselves to improve production without affecting animal welfare. This work investigates the influence that some climatic parameters such as Environment Temperature, Relative Humidity, Thermal excursion and Temperature–Humidity Index (THI), can have on milk quantity and quality in two different dairy species (buffaloes and cows) raised on the same farm. A further aim was to understand if THI threshold used for cows could also be used for buffaloes. The climatic parameters were recorded daily through a meteorological station located inside the farm. Milk quantity (converted into ECM) and quality (Fat Percentage—FP; Protein Percentage—PP; Somatic Cell Count—SCC) were measured. Data were analyzed with Spearman’s correlation index, separately for buffaloes and cows. The results indicate a greater sensitivity of cows to heat stress and a strong negative correlation of the ECM with meteorological data (p < 0.01). The results of this study may stimulate the use of integrated technologies (sensors, software) in the dairy sector, since the IoT (sensors, software) helps to enhance animal well-being and to optimize process costs, with a precision livestock farming approach.