Skyrmions are present in many models where the Higgs is a pseudo-Goldstone boson of a new global symmetry, depending on the symmetry breaking pattern. They are very heavy objects, in the mass range 10-100 TeV, and are stable over time. By performing the quantization of skyrmions in the presence of gauge fields, we show that the lightest skyrmion states tend to be electrically charged. On the other hand, their small annihilation cross-section make them long-lived, which poses a serious problem for cosmology. This issue is present in most of the existing little Higgs models. On the contrary, composite Higgs models are typically free of this problem because of a trivial homotopy or due to the fact that the new fermions share the same quantum numbers as the standard model quarks.