We have directly observed the electric-field-driven hot-electron distribution in high-mobility GaAs/AlGaAs heterostructures by detecting the grating-induced far-infrared Smith-Purcell emission. In samples with very low concentration the distribution develops a non-thermal shape at low electric fields due to the dominance of LO phonon emission. For the first time the average mean free path of the hot electrons is determined by studying the emission signal as a function of the grating period length.