By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the μ(I)-rheology.