We report direct measurements of hole spin lifetimes in ferromagnetic GaMnAs carried out by time- and polarization-resolved spectroscopy. Below the Curie temperature, ultrafast photoexcitation of GaMnAs with linearly polarized light is shown to create a nonequilibrium hole spin population via dynamical polarization of the holes through p-d exchange scattering with ferromagnetically ordered Mn spins. The system is then observed to relax in a distinct three-step recovery process: (i) a femtosecond hole spin relaxation, on the scale of 160-200 fs; (ii) a picosecond hole energy relaxation, on the scale of 1-2 ps; and (iii) a coherent, damped Mn spin precession with a period of 250 ps. The transient amplitude of the hole spin relaxation component diminishes with increasing temperature, directly following the ferromagnetic order of GaMnAs, while the hole energy amplitude shows negligible temperature change. Our results serve to establish the hole spin lifetimes in the ferromagnetic semiconductor GaMnAs, at the same time demonstrating a spectroscopic method for studying nonequilibrium hole spins in the presence of magnetic order and spin-exchange interaction.