ABSTRACT 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 current biases in planet dissipation of Alfvén waves. These waves are triggered by sub-surface convective motions and propagate along magnetic field lines. Here, we vary the magnetic field strength B0 and density ρ0 at the wind base (chromosphere), while keeping the same relative wave amplitude (0.1B0) and dissipation length-scale. Our simulations thus range from low plasma-β to high plasma-β (0.005–3.7). We find that our winds very quickly reach isothermal temperatures with mass-loss rates $\skew{2}\dot{M} \propto \rho _0^2$. We compare our results with Parker wind (PW) models and find that, in the high-β regime, both models agree. However, in the low-β regime, the PW underestimates the terminal velocity by around one order of magnitude and $\skew{2}\dot{M}$ by several orders of magnitude. We also find that M dwarfs could have chromospheres extending to 18 to 180 per cent of the stellar radius. We apply our model to the planet-hosting star GJ 436 and find, from X-ray observational constraints, $\skew{2}\dot{M}\lt 7.6\times 10^{-15}\, {\rm M}_{\odot }~\text{yr}^{-1}$. This is in agreement with values derived from the Lyman-α transit of GJ 436b, indicating that spectroscopic planetary transits could be used as a way to study stellar wind properties.