Galactic outflows of molecular gas are a common occurrence in galaxies and may represent a mechanism by which galaxies self-regulate their growth, redistributing gas that could otherwise have formed stars. We previously presented the first survey of molecular outflows at z > 4 toward a sample of massive, dusty galaxies. Here we characterize the physical properties of the molecular outflows discovered in our survey. Using low-redshift outflows as a training set, we find agreement at the factor of 2 level between several outflow rate estimates. We find molecular outflow rates of 150-800 M-circle dot yr(-1) and infer mass loading factors just below unity. Among the high-redshift sources, the molecular mass loading factor shows no strong correlations with any other measured quantity. The outflow energetics are consistent with expectations for momentum-driven winds with star formation as the driving source, with no need for energy-conserving phases. There is no evidence for active galactic nucleus activity in our sample, and while we cannot rule out deeply buried active galactic nuclei, their presence is not required to explain the outflow energetics, in contrast to nearby obscured galaxies with fast outflows. The fraction of the outflowing gas that will escape into the circumgalactic medium (CGM), though highly uncertain, may be as high as 50%. This nevertheless constitutes only a small fraction of the total cool CGM mass based on a comparison to z similar to 2-3 quasar absorption line studies, but could represent greater than or similar to 10% of the CGM metal mass. Our survey offers the first statistical characterization of molecular outflow properties in the very early universe.