At first, I think there is a difference between utilitarianism and hedonism in that first assumes some kind of utility which can be calculated and last simply puts that it's natural (we are not here for critique of what "natural" means, I just accept "natural state of mind" for a state of mind when a human is free from fears, in particular from shame) for people to strive for pleasure and avoid pain.
We know that Nietzsche criticised utilitarianism, actually hated it. Probably believed living according to its principles would result in passivity.
However, my treatmeant of hedonism assumes that (some) people sooner or later will be bored by doing all the same stuff and actually that hedonism is one of very few engines of progress (another one I could think of is curiosity). Since people want novelty they create new things and this does not seem nihilstic at all.
Since hedonism (at least my understanding of it) is not nihilstic, would Nietzsche be against it? Is there anything in Nietzsche living comments on this type of thinking and living?