That's right. It might be more insightful to consider it as propagating in space-time. The presence of the gravitational field results in curved world lines, or paths particles will follow. The effect of the field on the particles is on the momentum of the particles. The presence of mass results in the field, the field effects the momentum of particles. Force is dp/dt, or the change of momentum with time. Time of course, is a coordinate in 4-space. For photons in a gravitational field, the speed is c, but the momentum, p=h/wavelength, is effected by the field, so that c remains constant.