Dwarf galaxies, having lower masses and generally simpler merger histories, constitute unique environments for studying galactic evolution. One of the long-standing problems in the field has been the metal-mixing problem, which explores chemical evolution in galaxies and its relationship with its physical driving factors. Previous works have examined metal mixing in idealized dwarf galaxy simulations, where they successfully fit the spatial distribution of various metals in the Interstellar Medium (ISM) and its phases using analytic functions derivable from current galaxy evolution models. Here, we tackle the metal-mixing problem for cosmological dwarf galaxy simulations. Specifically, we survey three dwarf galaxies having dark matter halo masses of 1010, 1011, 1012 Msun. We examine the gas in the neutral phase of the ISM (T < 104 K) and realize that the said metal abundance distributions are still well-described by expected analytic functions. We also study the temporal evolution of abundance statistics and obtain a new analytical model for the same. Finally, we discover significant correlations among abundance statistics and some physical properties of interest - average star-formation rate, dark matter halo mass, and average Mach number. These findings are within expectation since the neutral ISM gas contributes strongly to star-formation in the galaxy.