The origin is freezing point depression. Broadly, salty water - and the water can come from skin moisture alone - has a lower water concentration (<100% water) than pure ice (100% water), so water tends to move to the area of lower concentration. (This is equivalent to the equilibrium melting point going down.) But this movement requires melting, which absorbs substantial energy corresponding to the latent heat and makes the system and the surroundings much colder. This translates into much more severe freezing of tissue than with ice alone. Make sense?