Is the Polar Ice Fields entirely RNG based like the Crypts or is there more to it? I know that you need to get lucky enough to pick up the frozen cookie before reaching the polar bear cub, but other than that I can't say I really understand much of whats going on.

yeah, totally random. Pretty much exactly like the crypts, but shorter. There are some prizes you can find wandering around, frozen tea, and such (you can see a list on SubetaLodge, ice field prizes).