Extensive experimentation on individual animals in respiration chambers has already been carried out to evaluate the potential of dietary changes and opportunities to mitigate CH4 emissions from ruminants. Although it is difficult to determine the air exchange rate of open barn spaces, measurements at the herd level should provide similarly reliable and robust results. The primary objective of this study was (1) to define a validity range (data classification criteria (DCC)) for the variables of wind velocity and wind direction during long-term measurements at barn level; and (2) to apply this validity range to a feeding trial in a naturally cross-flow ventilated dairy barn. The application of the DCC permitted quantification of CH4 and NH3 emissions during a feeding trial consisting of four periods. Differences between the control group (no supplement) and the experimental group fed a ration supplemented with condensed Acacia mearnsii tannins (CT) became apparent. Notably, CT concentrations of 1% and 3% of ration dry matter did not reduce CH4 emissions. In contrast, NH3 emissions decreased 34.5% when 3% CT was supplemented. The data confirm that quantification of trace gases in a naturally ventilated barn at the herd level is possible.