We present stellar metallicities in Leo I, Leo II, IC 1613, and Phoenix dwarf galaxies derived from medium (F390M) and broad (F555W, F814W) band photometry using the Wide Field Camera 3 (WFC3) instrument aboard the Hubble Space Telescope. We measured metallicity distribution functions (MDFs) in two ways, 1) matching stars to isochrones in color-color diagrams, and 2) solving for the best linear combination of synthetic populations to match the observed color-color diagram. The synthetic technique reduces the effect of photometric scatter, and produces MDFs 30-50 % narrower than the MDFs produced from individually matched stars. We fit the synthetic and individual MDFs to analytical chemical evolution models (CEM) to quantify the enrichment and the effect of gas flows within the galaxies. Additionally, we measure stellar metallicity gradients in Leo I and II. For IC 1613 and Phoenix our data do not have the radial extent to confirm a metallicity gradient for either galaxy. We find the MDF of Leo I (dwarf spheroidal) to be very peaked with a steep metal rich cutoff and an extended metal poor tail, while Leo II (dwarf spheroidal), Phoenix (dwarf transition) and IC 1613 (dwarf irregular) have wider, less peaked MDFs than Leo I. A simple CEM is not the best fit for any of our galaxies, therefore we also fit the `Best Accretion Model of Lynden-Bell 1975. For Leo II, IC 1613 and Phoenix we find similar accretion parameters for the CEM, even though they all have different effective yields, masses, star formation histories and morphologies. We suggest that the dynamical history of a galaxy is reflected in the MDF, where broad MDFs are seen in galaxies that have chemically evolved in relative isolation and narrowly peaked MDFs are seen in galaxies that have experienced more complicated dynamical interactions concurrent with their chemical evolution.