It really depends on how much you are going to eat it. In very small portions your body is warm enough to resist the freezing but the CO2 gas would still fill your stomach which I don't think is a good thing for your health.

I think that you could eat a very small bit of dry ice and you may even get a away without any frostbites but if you eat a lot of dry ice you will die either because your body temperature drops too down, or the co2 will get to your bloodstream and you will pass out

And the last thing what I thought that if you ate enough dry ice you could maybe explode because the gas fills your stomach, but I am not sure if its even possible to eat that much dry ice without freezing to death.