Cooling atoms by allowing them to equilibrate with cryogenic helium is a powerful tool which can be applied to any atomic species, and can produce very large samples of cold atoms (T ~ 500 mK). However, magnetically trapping these atoms has proved challenging. As a result only atoms with large magnetic moments have been trapped this way, and evaporative cooling of these species has proved too inefficient (due to their enhanced spin relaxation) to reach quantum degeneracy. In this talk I will describe recent work in which we demonstrate that buffer gas cooling can be used to trap atoms with magnetic moments of 2 Bohr magnetons, of which at least one species is known to be Bose-condensable by evaporative cooling. This trapping is made possible by the use of a novel cryovalve scheme and magnetic traps which push the limits of superconductor technology. At present this approach to trapping is limited by the dynamics of helium adsorbates within the apparatus. I will discuss the prospects for overcoming these limits and extending buffer gas trapping to 1 Bohr magneton atoms, which would allow for the trapping of the majority of atomic species with a single apparatus. We have also trapped atoms with large magnetic moments above 1 K, greatly simplifying the cryogenics required to study these species.