Context. The reported discovery of a cold (∼104 K) disc-like structure within the central 5 × 10-3 pc around the super-massive black hole at the centre of the Milk Way, Sagittarius A∗ (Sgr A∗), has challenged our understanding of the gas dynamics and thermodynamic state of the plasma in its immediate vicinity. State-of-the-art simulations do not agree on whether or not such a disc can indeed be a product of the multiple stellar wind interactions of the mass-losing stars in the region. Aims. The aims of this study are to constrain the conditions for the formation of a cold disc as a natural outcome of the system of the mass-losing stars orbiting around Sgr A∗, to investigate whether the disc is a transient or long-lasting structure, and to assess the validity of the model through direct comparisons with observations. Methods. We performed a set of hydrodynamic simulations of the observed Wolf-Rayet (WR) stars feeding Sgr A∗ using the finite- volume adaptive mesh refinement code Ramses. We focus, for the first time, on the impact of the chemical composition of the plasma emanating from the WR stars. Results. The simulations show that the chemical composition of the plasma affects the radiative cooling to a sufficient degree to impact the properties of the medium, such as density and temperature, and, as a consequence, the rate at which the material inflows onto Sgr A∗. We demonstrate that the formation of a cold disc from the stellar winds is possible for certain chemical compositions that are consistent with the current observational constraints. However, even in such cases, it is not possible to reproduce the reported properties of the observed disc-like structure, namely its inclination and the fluxes of its hydrogen recombination lines. Conclusions. We conclude that the stellar winds alone are not sufficient to form the cold disc around Sgr A∗ inferred from observations. Either relevant ingredients are still missing in the model, or the interpretation of the observed data needs to be revised.