Calculating snow avalanche impact pressure is an essential task for safe construction and hazard mapping in mountainous regions. Although avalanche-obstacle interaction crucially depends on the flow regime, practitioners mostly assume that impact pressure is similar to the dynamic pressure in inviscid fluids, that is, it is proportional to the square velocity weighted by an empirical drag coefficient. When fitting this coefficient to field measurements, one does not end up with a unique value, but with a range of possible values that cover more than one order of magnitude. In the absence of a physics-based framework, setting the right drag coefficient requires good working knowledge and experience from practitioners. Indeed, even for trained engineers it may be unclear how the impact pressure depends on the expected flow regime, on obstacle width, or on terrain configuration. To address these questions, we simulate the avalanche impact pressure on obstacles of varying geometry for four distinct avalanche flow regimes using the Discrete Element Method and a cohesive contact model. The results allow us to quantify the influence of the obstacle width and shape on the average impact pressure, as well as the detailed pressure distribution on the obstacle surface. Furthermore, we propose a novel method for estimating the drag coefficient based on simple geometrical considerations and key characteristics of avalanche flow. Our results are validated using experimental data from the Vallée de La Sionne test site, and make a step forward in the derivation of a physics-based framework for computing snow avalanche impact pressures for varied flow regimes depending on obstacle shape and dimensions.