The properties of electron and hole spins in InP/(Ga,In)P self-assembled quantum dots are studied through their coherent dynamics using time-resolved Kerr rotation. From these studies information about the g factor and dephasing of the spin excitations is extracted. The electron spin shows a behavior similar to that of electron spins in quantum dots of different material: The g factor is isotropic in the dot plane and with increasing applied magnetic field the spin dephasing accelerates due to variations in the dot ensemble. On the other hand, the hole spin demonstrates a behavior different from other dot systems. Namely, the signal decay on a time scale of about 100 ps does not depend on magnetic field, and the g factor is isotropic in the dot plane. These findings underline previous suggestions that only the electrons are well localized in the InP/(Ga,In)P quantum dots, while the holes are weakly confined and carry bulklike character.