The gravitational lens SDSS J1148+1930, also known as the Cosmic Horseshoe, is one of the biggest and most detailed Einstein rings ever observed.We use the forward reconstruction method implemented in the lens-fitting code LENSED to investigate in great detail the properties of the lens and background source. We model the lens with different mass distributions, focusing in particular on the determination of the slope of the dark-matter component. The inherent degeneracy between the lens slope and the source size can be broken when we can isolate separate components of each lensed image, as in this case. For an elliptical power-law model, κ(r)~r-t, the results favour a flatter-than-isothermal slope with amaximum-likelihood value of t=0.08. Instead, when we consider the contribution of the baryonic matter separately, the maximum-likelihood value of the slope of the dark-matter component is t = 0.31 or t = 0.44, depending on the assumed initial mass function. We discuss the origin of this result by analysing in detail how the images and the sources change when the slope t changes. We also demonstrate that these slope values at the Einstein radius are not inconsistent with the recent forecast from the theory of structure formation in the ΛCDM model.