Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This also has an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable, and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated delayed-detached eddy simulation model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries although the contribution of different momentum flux terms differs. These results represent a further step toward a deeper understanding the drag of complex-shaped particles.