  Exoplanets hosting M dwarfs are the best targets to characterize Earth-like
or super-Earth planetary atmospheres with the James Webb Space Telescope
(JWST). We determine detailed stellar parameters ($T_{\rm eff}$, log$g$, and
$\xi$) and individual abundances of twelve elements for four cool M dwarfs
hosting exoplanets TOI-1685, GJ 436, GJ 3470, and TOI-2445, scheduled for
future observations by the JWST. The analysis utilizes high-resolution
near-infrared spectra from the SDSS-IV APOGEE survey between 1.51-1.69$\mu$.
Based on 1D-LTE plane-parallel models, we find that TOI-2445 is slightly
metal-poor ([Fe/H] = -0.16$\pm$0.09), while TOI-1685, GJ 436 and GJ 3470 are
more metal-rich ([Fe/H] = 0.06$\pm$0.18, 0.10$\pm$0.20 dex, 0.25$\pm$0.15). The
derived C/O ratios for TOI-2445, TOI-1685, GJ 436, and GJ 3470 are
0.526$\pm$0.027, 0.558$\pm$0.097, 0.561$\pm$0.029, and 0.638$\pm$0.015,
respectively. From results for 28 M dwarfs analyzed homogeneously from APOGEE
spectra, we find exoplanet-hosting M dwarfs exhibit a C/O abundance ratio
approximately 0.01 to 0.05 higher than those with non-detected exoplanets, at
limits of a statistically significant offset. A linear regression of [Fe/H]
\textit{vs.} C/O distribution reveals a noticeable difference in the angular
coefficient between FGK dwarfs (0.27) and M dwarfs (0.13). Assuming our
abundance ratios of Ca/Mg, Si/Mg, Al/Mg, and Fe/Mg, we determine a mass of
3.276$^{+0.448}_{-0.419}$$M_{\oplus}$ for TOI-2445 b, having density
(6.793$^{+0.005}_{-0.099}$ g.cm$^{-3}$) and core mass fraction
(0.329$_{-0.049}^{+0.028}$) very similar to Earth's. We also present an atlas
of 113 well-defined spectral lines to analyze M dwarfs in the $H$-band and a
comprehensive evaluation of uncertainties from variations in the atmospheric
parameters, signal-to-noise, and pseudo-continuum.
