We present the stacking analysis of a sample of 48 quasi-stellar objects (QSOs) at 4.5<z<7.1 detected by the Atacama Large Millimetre Array (ALMA) in the [CII] {lambda}158um emission line to investigate the presence and the properties of massive, cold outflows associated with broad wings in the [CII] profile. The high sensitivity reached through this analysis allows us to reveal very broad [CII] wings tracing the presence of outflows with velocities in excess of 1000km/s. We find that the luminosity of the broad [CII] emission increases with LAGN, while it does not significantly depend on the star formation rate of the host galaxy, indicating that the central active galactic nucleus (AGN) is the main driving mechanism of the [CII] outflows in these powerful, distant QSOs. From the stack of the ALMA cubes, we derive an average outflow spatial extent of ~3.5kpc. The average atomic neutral mass outflow rate inferred from the stack of the whole sample is dM_out_/dt~100M_{sun}_/yr, while for the most luminous systems it increases to ~200M_{sun}_/yr. The associated outflow kinetic power is about 0.1% of L_AGN_, while the outflow momentum rate is ~L_AGN_/c or lower, suggesting that these outflows are either driven by radiation pressure onto dusty clouds or, alternatively, are driven by the nuclear wind and energy conserving but with low coupling with the interstellar medium. We discuss the implications of the resulting feedback effect on galaxy evolution in the early Universe.