We report on the discovery of HAT-P-10b, one of the lowest mass (0.487+/-0.018M_J_) transiting extrasolar planets (TEPs) discovered to date by transit searches. HAT-P-10b orbits the moderately bright V=11.89 K dwarf GSC 02340-01714, with a period P=3.7224747+/-0.0000065d, transit epoch T_c_=2454759.68683+/-0.00016(BJD), and duration 0.1090+/-0.0008d. HAT-P-10b has a radius of 1.005^+0.032^-0.027_R_J yielding a mean density of 0.594+/-0.052g/cm^3^. Comparing these observations with recent theoretical models we find that HAT-P-10b is consistent with a ~4.5Gyr, almost pure hydrogen and helium gas giant planet with a 10M_{earth} core. With an equilibrium temperature of T_eq=1020+/-17K, HAT-P-10b is one of the coldest TEPs. Curiously, its Safronov number {Theta}=0.053+/-0.002 falls close to the dividing line between the two suggested TEP populations.