We present the stacking analysis of a sample of 48 QSOs at 4.5<z<7.1 detected by ALMA in the [CII] 158 micron line to investigate the presence and the properties of massive, cold outflows traced by broad [CII] wings. We reveal very broad [CII] wings tracing the presence of outflows with velocities in excess of 1000 km/s. We find that the luminosity of the broad [CII] emission increases with LAGN, while it does not significantly depend on the SFR of the host galaxy, indicating that the central 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 ~3.5 kpc. The average mass outflow rate inferred from the whole sample stack is ~ 100 Msun/yr, while for the most luminous systems it increases to ~200 Msun/yr. The associated outflow kinetic power is about 0.1% of LAGN, while the outflow momentum rate is about LAGN/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 ISM. We discuss the implications of the resulting feedback effect on galaxy evolution in the early Universe.