When you apply or add salt to very cold ice the ice will begin to melt.
When added to ice the salt first dissolves in the film of liquid water that is always present on the surface, thereby lowering its freezing point below the ices temperature.
The ice that is in contact with the salty water therefore melts, creating more liquid water, which dissolves more salt, thereby causing more ice to melt.
Ice forms at a temperature of 32 F and can get even colder than that.
The ice can get as cold as it is outside so if you have a temperature of -100 F then the i can get that cold as well.
Once the ice gets above 32 F then it can begin to melt but ice can get as cold as the temperature that is surrounding it can.
Ice can sublimate at -10 F degrees or even below in some cases.
Especially dry ice which can sublimate at -100 F degrees.
Ice can and does sometimes evaporate without melting into a liquid first.
When ice evaporates without melting into liquid the process is known as sublimation.
Dry ice is a great example of ice that mostly evaporates without melting and it looks like steam when the sublimation of the ice is occurring.
The process of sublimation is most often used to describe the process of snow and ice changing into water vapor in the air without first melting into water.
"Dry ice" is actually solid, frozen carbon dioxide, which happens to sublimate, or turn to gas, at a chilly -78.5 °C (-109.3°F)
Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state.
An example of Sublimation in the picture below of dry ice going through the process of sublimation which is the process of ice evaporating without melting.