In the present work, we analyze magnetized solar-like stellar winds and their dependence on the plasma-$\beta$ parameter (the ratio between thermal and magnetic energy densities) by means of self-consistent three-dimensional (3D) magnetohydrodynamics (MHD) numerical simulations. We analyze winds with polar magnetic field intensities ranging from $1$ to $20$~G. By solving the fully ideal 3D MHD equations, we show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. The Lorentz force leads naturally to a latitude-dependent wind: the steady wind presents a bi-modal structure with fast and slow velocities, similar to the observed bi-modality of the velocity of the solar wind.