  M dwarf stars are currently the main targets in searches for potentially
habitable planets. However, their winds have been suggested to be harmful to
planetary atmospheres. Here, in order to better understand the winds of M
dwarfs and also infer their physical properties, we perform a one-dimensional
magnetohydrodynamic parametric study of winds of M dwarfs that are heated by
dissipation of Alfv\'en waves. These waves are triggered by sub-surface
convective motions and propagate along magnetic field lines. Here, we vary the
magnetic field strength and density at the wind base (chromosphere), while
keeping the same relative wave amplitude ($0.1 B_0$) and dissipation
lenghtscale. We find that our winds very quickly reach isothermal temperatures
with mass-loss rates proportional to base density square. We compare our
results with Parker wind models and find that, in the high-beta regime, both
models agree. However, in the low-beta regime, the Parker wind underestimates
the terminal velocity by around one order of magnitude and mass-loss rate by
several orders of magnitude. We also find that M dwarfs could have
chromospheres extending to 18% to 180% of the stellar radius. We apply our
model to the planet-hosting star GJ 436 and find, from X-ray observational
constraints, $\dot{M}<7.6\times 10^{-15}\,M_{\odot}~\text{yr}^{-1}$. This is in
agreement with values derived from the Lyman-alpha transit of GJ 436b,
indicating that spectroscopic planetary transits could be used as a way to
study stellar wind properties.
