Do snakes get dizzy?
Probably don't do any experiments that involve shoving reptiles in a sack and swinging them around your head, as someone will surely call the ASPCA on you.

The type of dizziness that is associated with spinning around is called "vertigo". From wikipedia:


  Repetitive spinning, as in familiar childhood games, can induce short-lived vertigo by disrupting the inertia of the fluid in the vestibular system


So then from a physiological perspective the question is, do snakes have fluid in their ears like people do? And a quick review of snake physiology seems to suggest that they do.

Thus, I'm going to put forward the tentative hypothesis that yes, snakes can get dizzy, but it's still probably very different from you think of as dizziness.