neutrinos are not affected by gravity on the subatomic scale
Where do you get this idea? It's not a part of mainstream physics.
One of the main ideas behind general relativity is that gravity isn't just another force battling it out in the arena of physics; it is the arena. That is, gravity is really just the geometry of spacetime, and anything (including a neutrino field) in spacetime is experiencing that geometry.
So no, standard physics does not predict that neutrinos will be able to escape a black hole. Instead, standard physics predicts that everything that enters a black hole's horizon will be unable to exit the horizon, including neutrinos. No one has done an experiment that can test this theory because we don't have very good neutrino telescopes or very good access to black holes. And it's possible that standard physics is wrong. But that's all we can say for now.
EDIT: In the comments below, the OP points out the underlying confusion that led to this question, which is the role of gravitons in black-hole physics. First of all, gravitons are (as @probably_someone points out) not really a part of mainstream physics. In particular, we don't know how to formulate a complete working theory of gravity using quantum field theory. We can quantize linearized gravity, which is the basic reason anyone really bothers to talk about gravitons, but that doesn't extend to nonlinear gravitational systems. And that's the key point: black holes are very nonlinear (unless you're very far away).
One consequence of this is that you can't model a black hole as a particle that interacts with other particles via exchange of gravitons. That's just not how our current theory of physics works. There's a related question with a very nice answer here, where Jerry Schirmer points out that the graviton is an excitation of the gravitational field, and not the field itself — but it's the field that makes a black hole, not its excitations. You might want to appeal to quantum field theory in curved spacetime, but even then, you basically assume a background curvature to spacetime. And it's that background curvature that affects the motion of the neutrino and traps it inside the horizon.