The present paper elaborates on the cold injection scheme, which was recently proposed in the context of laser wakefield acceleration (Davoine et al 2009 Phys. Rev. Lett. 102 065001). This scheme allows one to inject a bunch of electrons into a laser wakefield, which is possible thanks to the collision between the main and a counter-propagating laser pulse. Unlike in the conventional colliding pulse schemes, in this process, a beatwave is created during the collision, which allows the injection of electrons with negligible heating. In this paper, we show that the injection of on-axis electrons observed in simulations is well described by a one-dimensional (1D) model, as long as conditions given here are satisfied. Injection of off-axis electrons is also influenced by transverse effects, but the basic mechanisms remain the same. Then, a comparison with the conventional colliding pulse schemes shows that each scheme can occur in different regimes. In particular, cold injection proves to be more interesting regarding the energy spread issue. Indeed, the simulations demonstrate that electron bunches with sub-MeV absolute energy spreads can be injected, leading, after acceleration, to electrons at several GeV and relative energy spread below 1%.