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As cool clouds are entrained by a hot supersonic galactic wind, they may be shredded by hydrodynamical instabilities and incorporated into the hot flow. One-dimensional steady-state calculations show how cool cloud entrainment affects the bulk thermodynamics and kinematics of the hot gas: mass-loading decelerates the hot flow and changes its entropy. Here, we investigate the stability of mass-loaded hot winds using both perturbation analysis and 3D time-dependent radiative hydrodynamical simulations. We show that mass-loading is stable over a broad range of parameters and that the 1D time-steady analytic solutions exactly reproduce the 3D time-dependent calculations, provided that the flow does not decelerate sufficiently to become subsonic. For higher values of the mass-loading, the flow develops a second sonic point, with the first being at the edge of the wind-driving region. Strong deceleration increases the wind density and the flow becomes radiative, undergoing a thermal instability to form elongated dense cometary filaments. We explore the mass-loading parameters required to trigger this behaviour. For certain approximations, we can derive analytic criteria. In general, a mass-loading rate similar to the initial hot-mass outflow rate is required. In this sense, the destruction of small cool clouds by a hot flow may ultimately spontaneously generate fast cool filaments, as observed in starburst winds. Lastly, we find that the kinematics of filaments is sensitive to the slope of the mass-loading function. Filaments move faster than the surrounding wind if mass-loading is over long distances whereas filaments move slower than their surroundings if mass-loading is abrupt. [ABSTRACT FROM AUTHOR]