Katabatic flows over alpine mountainous terrain differ from their forested or bare slope counterparts due to the presence of well-ventilated, short vegetation. The impact of a grass canopy and larger-scale pressure perturbations on the one-dimensional mean momentum balance is explored via theory and field measurements. The model presented here reproduces the measured velocity jet shape and turbulent flux gradients. These two features imply that even when Monin-Obuhkov similarity theory breaks down, its use for a stability adjusted mixing length remains effective to first order. Results reveal that outer layer pressure effects can be significant under low-speed wind conditions at the top of the thin katabatic layer when larger variations in the wind direction are observed. An analytical expression to estimate the jet height, which can be utilized in large-scale weather prediction models, shows the importance of including canopy effects for the thin katabatic flow region above the vegetation.