As to snow tires ...
The loader's tires are already pretty aggressive, so not sure how much a snowtire would help ( though will look into it ).
Since the grooves are rigid, snow and ice will pack into it no matter what. When that happens though, they might as well be slicks.
The advantage of a chain ( in addition to being able to penetrate the ice ) is that it's loose, so it cannot pack up.
My thinking with the rubber chain is that though it will not penetrate the ice, it is still loose so the packing up won't happen.