  The interaction between the strong winds in stellar colliding-wind binary
(CWB) systems produces two shock fronts, delimiting the wind collision region
(WCR). There, particles are expected to be accelerated mainly via diffusive
shock acceleration (DSA). We investigate the injection and the acceleration of
protons in typical CWB systems by means of Monte Carlo simulations, with both a
test-particle approach and a non-linear method modelling a shock locally
modified by the backreaction of the accelerated protons. We use
magnetohydrodynamic simulations to determine the background plasma in the WCR
and its vicinity. This allows us to consider particle acceleration at both
shocks, on either side of the WCR, with a realistic large-scale magnetic field.
We highlight the possible effects of particle acceleration on the local shock
profiles at the WCR. We include the effect of magnetic field amplification due
to resonant streaming instability (RSI), and compare results without and with
the backreaction of the accelerated protons. In the latter case we find a lower
flux of the non-thermal proton population, and a considerable magnetic field
amplification. This would significantly increase the synchrotron losses of
relativistic electrons accelerated in CWB systems, lowering the maximal energy
they can reach and strongly reducing the inverse Compton fluxes. As a result,
$\gamma$-rays from CWBs would be predominantly due to the decay of neutral
pions produced in nucleon-nucleon collisions. This might provide a way to
explain why, in the vast majority of cases, CWB systems have not been
identified as $\gamma$-ray sources, while they emit synchrotron radiation.
