We propose a dynamic controller for position tracking of a point-mass load attached to an omnidirectional aerial vehicle by means of a cable. Both the load and the aerial vehicle are subject to unknown wind forces. We model the dynamics of the slung-load system and put it into canonical form, i.e., a form which is independent of the system's physical parameters. Following a backstepping strategy, we design a dynamic control law for the canonical system that contains four estimators, since each of the two wind disturbances has two separate effects: an effect on the linear acceleration and another on the angular acceleration. Loosely speaking, the difference between the wind forces is an input-additive disturbance, while the wind force on the load is not, which makes removing the wind force on the load nontrivial. We identify conditions on the desired position trajectory and on the wind on the load, which guarantee that a well-defined equilibrium trajectory exists. The designed controller guarantees simultaneously that the latter trajectory is asymptotically tracked and the cable remains taut, provided that the system is initialized in a suitable set. Simulations illustrate our results.