We measure electron tunneling via discrete energy levels in ferromagnetic cobalt particles that are less than 4 nm in diameter, using nonmagnetic electrodes. Because of magnetic anisotropy, the energy of each tunneling resonance shifts as an applied magnetic field rotates the particle's magnetic moment. We see both spin-increasing and decreasing tunneling transitions, but do not observe the spin degeneracy at small magnetic fields seen previously in nonmagnetic materials. The tunneling spectrum is denser than predicted for independent electrons, possibly due to spin-wave excitations.