Yes, in the sense that the rubber will get hard and brittle.
If by 'freeze' you mean the formal definition, which is to form
actual crystals, as water does when it freezes, then the rubber won't
freeze.
You should know that when you drop the rubber into the liquid,
the liquid will boil off very quickly for a while even though it's in a
dewar. That's because heat will flow straight from the rubber into the
liquid. The boil-off can be fast enough to make a lot of drops of
liquid splatter around. So you absolutely should not do this without
some sort of protective eye-glasses.
Mike W.
(published on 10/22/2007)