^I doubt 'Fire and Ice' drew much, if anything directly from 'Dune'. Any similarities are more likely the result of both authors drawing from a common historical source. The politics of Dune makes no bones about taking it's inspiration from Medieval European court intrigues and the Senate plots of Ancient Rome.
The only other similarity I can see is the archetypal hero's journey, which is of course not something Martin would have needed to borrow from Herbert.
Indeed, exactly who the "hero" on their journey is in 'Fire and Ice' is a bit hard to figure out since all the one's you'd expect have mostly been killed off. Personally my money is on Aria, Tyrion *and* Daenerys. I mean who says there can only be one "hero's journey" per story?