Cosmological analyses with type Ia supernovae (SNe Ia) often assume a single empirical relation between color and luminosity ($β$) and do not account for varying host-galaxy dust properties. However, from studies of dust in large samples of galaxies, it is known that dust attenuation can vary significantly. Here we take advantage of state-of-the-art modeling of galaxy properties to characterize dust parameters (dust attenuation $A_V$, and a parameter describing the dust law slope $R_V$) for the Dark Energy Survey (DES) SN Ia host galaxies using the publicly available \texttt{BAGPIPES} code. Utilizing optical and infrared data of the hosts alone, we find three key aspects of host dust that impact SN Ia cosmology: 1) there exists a large range ($∼1-6$) of host $R_V$ 2) high stellar mass hosts have $R_V$ on average $∼0.7$ lower than that of low-mass hosts 3) there is a significant ($>3σ$) correlation between the Hubble diagram residuals of red SNe Ia that when corrected for reduces scatter by $∼13\%$ and the significance of the ``mass step'' to $∼1σ$. These represent independent confirmations of recent predictions based on dust that attempted to explain the puzzling ``mass step'' and intrinsic scatter ($σ_{\rm int}$) in SN Ia analyses. We also find that red-sequence galaxies have both lower and more peaked dust law slope distributions on average in comparison to non red-sequence galaxies. We find that the SN Ia $β$ and $σ_{\rm int}$ both differ by $>3σ$ when determined separately for red-sequence galaxy and all other galaxy hosts. The agreement between fitted host-$R_V$ and SN Ia $β$ \& $σ_{\rm int}$ suggests that host dust properties play a major role in SN Ia color-luminosity standardization and supports the claim that SN Ia intrinsic scatter is driven by $R_V$ variation.