  Local Group (LG) galaxies have relatively accurate SFHs and metallicity
evolution derived from resolved CMD modeling, and thus offer a unique
opportunity to explore the efficacy of estimating stellar mass M$_{\star}$ of
real galaxies based on integrated stellar luminosities. Building on the SFHs
and metallicity evolution of 40 LG dwarf galaxies, we carried out a
comprehensive study of the influence of SFHs, metallicity evolution, and dust
extinction on the UV-to-NIR color-$M/L$
(color-log$\Upsilon_{\star}$($\lambda$)) relations and M$_{\star}$ estimation
of local universe galaxies. We find that: The LG galaxies follow
color-log$\Upsilon_{\star}$($\lambda$) relations that fall in between the ones
calibrated by previous studies; Optical color-log$\Upsilon_{\star}$($\lambda$)
relations at higher metallicities ([M/H]) are generally broader and steeper;
The SFH "concentration" does not significantly affect the
color-log$\Upsilon_{\star}$($\lambda$) relations; Light-weighted ages and [M/H]
together constrain log$\Upsilon_{\star}$($\lambda$) with uncertainties ranging
from $\lesssim$ 0.1 dex for the NIR up to 0.2 dex for the optical passbands;
Metallicity evolution induces significant uncertainties to the optical but not
NIR $\Upsilon_{\star}$($\lambda$) at given light-weighted ages and [M/H]; The
$V$ band is the ideal luminance passband for estimating
$\Upsilon_{\star}$($\lambda$) from single colors, because the combinations of
$\Upsilon_{\star}$($V$) and optical colors such as $B-V$ and $g-r$ exhibit the
weakest systematic dependence on SFHs, [M/H] and dust extinction; Without any
prior assumption on SFHs, M$_{\star}$ is constrained with biases $\lesssim$ 0.3
dex by the optical-to-NIR SED fitting. Optical passbands alone constrain
M$_{\star}$ with biases $\lesssim$ 0.4 dex (or $\lesssim$ 0.6 dex) when dust
extinction is fixed (or variable) in SED fitting. [abridged]
