It is well established that MgII absorption lines detected in background quasar spectra arise from gas structures associated with foreground galaxies. The degree to which galaxy evolution is driven by the gas cycling through halos is highly uncertain because their gas mass density is poorly constrained. Fitting the MgII equivalent width (W) distribution with a Schechter function and applying the N(HI)-W correlation of Menard & Chelouche, we computed Omega(HI)_MgII ~ Omega(HI)_halo =(1.41 +0.75 -0.44)x10^-4 for 0.4<z<1.4. We exclude DLAs from our calculations so that Omega(HI)_halo comprises accreting and/or outflowing halo gas not locked up in cold neutral clouds. We deduce the cosmic HI gas mass density fraction in galactic halos traced by MgII absorption is Omega(HI)_halo/Omega(HI)_DLA=15% and Omega(HI)_halo/Omega_b=0.3%. Citing several lines of evidence, we propose infall/accretion material is sampled by small W whereas outflow/winds are sampled by large W, and find Omega(HI)_infall is consistent with Omega(HI)_outflow for bifurcation at W=1.23^{+0.15}_{-0.28}AA; cold accretion would then comprise no more than ~7% of of the total HI mass density. We discuss evidence that (1) the total HI mass cycling through halos remains fairly constant with cosmic time and that the accretion of HI gas sustains galaxy winds, and (2) evolution in the cosmic star formation rate depends primarily on the rate at which cool HI gas cycles through halos.