  Galactic cosmic rays are energetic particles important in the context of
life. Many works have investigated the propagation of Galactic cosmic rays
through the Sun's heliosphere. However, the cosmic ray fluxes in M dwarf
systems are still poorly known. Studying the propagation of Galactic cosmic
rays through the astrospheres of M dwarfs is important to understand the effect
on their orbiting planets. Here, we focus on the planetary system GJ 436. We
perform simulations using a combined 1D cosmic ray transport model and 1D
Alfv\'en-wave-driven stellar wind model. We use two stellar wind set-ups: one
more magnetically-dominated and the other more thermally-dominated. Although
our stellar winds have similar magnetic field and velocity profiles, they have
mass-loss rates two orders of magnitude different. Because of this, they give
rise to two different astrosphere sizes, one ten times larger than the other.
The magnetically-dominated wind modulates the Galactic cosmic rays more at
distances < 0.2 au than the thermally-dominated wind due to a higher local wind
velocity. Between 0.2 and 1 au the fluxes for both cases start to converge.
However, for distances > 10 au, spatial diffusion dominates, and the flux of
GeV cosmic rays is almost unmodulated. We find, irrespective of the wind
regime, that the flux of Galactic cosmic rays in the habitable zone of GJ 436
(0.2 - 0.4 au) is comparable with intensities observed at Earth. On the other
hand, around GJ 436 b (0.028 au), both wind regimes predict Galactic cosmic ray
fluxes that are approximately $10^4$ times smaller than the values observed at
Earth.
