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Although it is intuitively and qualitatively known that a treaded tire has a larger drawbar pull than a smooth tire, little is known quantitatively about all the interfacial forces and the origins of these forces of a treaded tire traversing a snow cover. There have been relatively few studies regarding the quantitative effects of tread pattern on tire-snow interaction due to the complexity of the tread pattern, the enormous amount of computational resources needed for high-fidelity numerical simulations, and the difficulty of measuring all the interfacial forces between a tire that is much harder than snow. The purpose of this paper is to understand the effects of a simplified tread pattern of a two-dimensional rigid tire on the interfacial forces between a tire and low-density snow. The parameters to vary included the wheel load, as well as a full-range of longitudinal slip.