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Bosonic field theories with self interactions alongside gravity, generally admit bound states known as solitons. Depending upon the spin nature of the field, they can even carry macroscopic intrinsic spin polarization. Focusing on the SU($2$) case, we describe polarized solitons in non-Abelian theories with a heavy Higgs, which we refer to as `Yang-Mills stars'. Owing to both kinds of self-interactions; repulsive ones arising due to the Yang-Mills structure, while attractive ones arising due to the Higgs exchange; we can have a diverse zoo of solitons. Depending upon various parameters of the theory such as the mass of the Yang-Mills vector fields $m$, mass of the dark Higgs field $M_φ$, and the gauge coupling constant $g$, these objects can be astrophysically large with varying size and mass, and carry large intrinsic spin and/or iso-spin giving rise to interesting phenomenological implications. Even for vector mass as large as $m \simeq 10$ eV, we can accommodate gauge couplings $g \lesssim 10^{-4}-10^{-5}$, still evading Bullet cluster constraints. For these parameters, there may exist cosmologically long lived solitons having radii as large as $r_{s} \sim 10^{5}\,R_{\odot}$ and masses $M_{s} \sim 10 M_{\odot}$, carrying $M_{s}/m \sim 10^{66}$ amounts of intrinsic spin and iso-spin polarization. As a subset of the space of soliton solutions in the SU($2$) Higgs model, in the end we also explicitly discuss solitons in the Abelian Higgs model.