The dissolving of ammonium nitrate is often used in an instant cold pack used to relieve swelling.

. If the process is an endothermic reaction, then why does it feel cold to the touch instead of hot?

Endothermic reaction means that the process takes in heat. When breaking the cold pack, heat is taken in from the surroundings to dissolve the ammonium nitrate. Due to this loss of heat, the pack feels cold.

ummm, the answer to your question is basically in your reaction name

endothermic reaction means that heat is being absorbed during the reaction, so when you touch the ammonium nitrate cold pack, the pack sucks heat from your hand, making it cold