We use simulations of merging galaxies to explore the sensitivity of the morphology of tidal tails to variations of the halo mass distributions in the parent galaxies. Our goal is to constrain the mass of dark halos in well-known merging pairs. We concentrate on prograde encounters between equal-mass galaxies that represent the best cases for creating tidal tails, but we also look at systems with different relative orientations, orbital energies, and mass ratios. As the mass and extent of the dark halo increase in the model galaxies, the resulting tidal tails become shorter, less massive, and less striking, even under the most favorable conditions for producing these features. Our simulations imply that the observed merging galaxies with long tidal tails (similar to 50-100 kpc) such as NGC 4038/39 (the Antennae) and NGC 7252 probably have halo: disk + bulge mass ratios less than 10:1. These results conflict with the favored values of the dark halo mass of the Milky Way derived from satellite kinematics and the timing argument, which give a halo: disk + bulge mass ratio of similar to 30:1. However, the lower bound of the estimated dark halo mass in the Milky Way (mass ratio similar to 10:1) is still consistent with the inferred tidal tail galaxy masses. Our results also conflict with the expectations of Omega = 1 cosmologies such as CDM, which predict much more massive and extended dark halos.