Magnetocontrollable droplet mobility on surfaces of both solids and simple fluids have been widely used in a wide range of applications. However, little is understood about the effect of the magnetic field on the wettability and mobility of droplets on structured fluids. Here, we report the manipulation of the dynamic behaviors of water droplets on a film of thermotropic liquid crystals (LCs). We find that the static wetting behavior and static friction of water droplets on a 4’-octyl-4-biphenylcarbonitrile (8CB) film strongly depend on the LC mesophases, and that a magnetic field caused no measurable change to these properties. However, we find that the droplet dynamics can be affected by a magnetic field as it slides on a nematic 8CB film, but not on isotropic 8CB, and is dependent on both the direction and strength of the magnetic field. By measuring the dynamic friction of a droplet sliding on a nematic 8CB film, we find that a magnetic field alters the internal orientational ordering of the 8CB which in turn affects its viscosity. We support this interpretation with a scaling argument using the LC magnetic coherence length that includes (i) the elastic energy from the long-range orientational ordering of 8CB and (ii) the free energy from the interaction between 8CB and a magnetic field. Overall, these results advance our understanding of droplet mobility on LC films and enable new designs for responsive surfaces that can manipulate the mobility of water droplets.