Re: Why does salt and ice on skin mimic feelings of frosbite or burn?

You are quite right -- what you are experiencing is a frostbite.
You are pretty much right about the mechanism as well.

The freezing point of saturated salt solution is about -21 deg C or -5 deg 
F. If ice above this temperature comes into contact with salt in the solid 
form, it will melt, dissolving the salt as it goes. But it takes a lot of 
heat to melt ice -- the latent heat of fusion. In the experiment you 
describe, that heat can only come from your body, fairly rapidly, and in 
fairly large quantities.