I've read that neutrinos in supernova can be affected by "neutrino refraction." Is this analagous to the refraction of light, and if so, is the speed of these neutrinos similarly reduced from their near c speeds via this index of refraction?
Now, it is generally true that the "speed" (or, more accurately, the dispersion relation) of any particle is affected by a medium, where it travels. Well, of course, if the particle interacts with the medium.
For neutrinos the "slowing down" itself is absolutely negligible even in very dense media. What is important is that interaction of the electron neutrino with ordinary matter is much stronger, so it affects the patterns of neutrino oscillations -- the effect is known as MSW effect.
Finally, this is not particularly related to supernovae. The idea behind interest in supernovae is that during an explosion there are a lot of neutrinos so one must account for the "neutrino matter" and its effect on oscillations as well.