The second virial coefficient of water is calculated at low temperature by considering full quantum statistical mechanical effects. At low enough temperatures experimental results are limited and molecular models can be used for accurate extrapolation. In doing so, one must separate deficiencies of the intermolecular potential from limitations of the simulation methodology such as the neglect of higher-order quantum corrections. Effective classical potentials may be used to understand the limitations of classical simulation. In this work we calculate the exact quantum statistical mechanical second virial coefficient and find that using a semiclassical form for the effective classical potential we are able to nearly reproduce the exact quantum statistical results. This approach provides a significant improvement to conventional first order expansions of the second virial coefficient.