The winds observed in the pre-main-sequence phase of intermediate-mass young stars are discussed in light of a model originally developed by Mestel for describing stellar winds ejected by rotating stars. In addition to the acceleration mechanisms of thermal expansion and stellar radiation pressure, which typically play an important role in driving the winds of low- and high-mass stars, respectively, centrifugal acceleration by a corotating magnetic field and the presence of hydromagnetic waves are taken into account. The relevance of these mechanisms for the acceleration of stellar winds from the surface of young stars is discussed in the context of growing evidence for the presence of magnetic fields and surface convection in pre-main-sequence evolutionary phases. In the particular case of Herbig Ae/Be stars, the deposition of a fraction of the convection energy in Alfven waves seems to be required in order to explain the winds observed in these pre-main-sequence objects. Under some simplifying assumptions, the velocity and density fields around the central stellar object are derived and the emerging line profiles are computed. A test case is discussed in which the observed line profiles of the prototypical object AB Aur are used to constrain the model parameters, showing that the magnetic rotator model offers a physically consistent description of this system.