Increasing concerns regarding environmental impacts of animal production require a better understanding of the factors that influence nitrogen (N) excretion by animals and the processes that influence N volatilization into ammonia (NH3) and nitrous oxide (N2O) from manure. The objective of this study was to evaluate the influence of diet characteristics and climatic factors on manure composition, as well as the resulting NH3 and N2O emissions in the barn and during storage of a straw-based litter system. Two groups of three dairy cows were housed in mechanically ventilated rooms and fed with a grass-based diet (GD) or a total mixed diet (MD). The resulting solid manures were stored in ventilated tunnels. The experiment was conducted in autumn (AUT) and spring (SPR). NH3 and N2O emissions were recorded continuously (28 days in the barn, 85 days for storage). NH3–N emissions in the barn were higher for GD-AUT than for MD-AUT, which was consistent with the larger and unbalanced amount of crude and degradable protein in GD, and corroborated by higher milk urea N contents. More than 80% of the NH3–N volatilization occurred during the first week of manure storage, when the temperature of the manure heap peaked. N2O–N emissions were negligible in the barn. During storage, N2O–N emissions peaked immediately after the first week. Higher N2O–N emissions were related to higher rainfall, which may have increased the moisture content and decreased the temperature of the manure heap, thus generating the conditions necessary for nitrification and denitrification processes.