A major focus in infrasound research is the inclusion of realistic atmospheric flows in numerical propagation models. This usually encompasses temperature gradients and horizontal wind components, which create atmospheric waveguides. Additionally, gravity waves lead to small-scale variations of the ambient wind in the middle atmosphere, between 10 and 100 km in altitude. Using an internal gravity wave model from the literature [Gardner, J. Atmos. Terr. Phys. (1996)], we parametrize random fluctuations of the wind profiles, where the initial background state is based on a published case study [Sabatini et al., J. Acoust. Soc. Am. (2016)]. Acoustic propagation from an impulsive point source located at the ground is then modelled with solvers of the PLetma package [Khodr et al., J. Acoust. Soc. Am. (2021)], namely, ray tracing, normal modes, one-way equation and FDTD, for frequencies higher than 0.01 Hz. Cases with and without wind are considered, and propagation effects are investigated by a sensitivity analysis on source parameters and characteristics of the gravity wave. [This work was conducted within the framework of LETMA, a Contractual Research Laboratory shared between CEA, CNRS, Ecole Centrale de Lyon, C-Innov, and Sorbonne Université.]