Ice feels very cold to you because it is around 36 degrees Celsius below your body temperature, it is a fairly large difference.
Ice is one of the solid structures of water and is crystalline! It is stabilised by a network of molecules forming bonds to each other and limiting their movements and vibrations.
It’s all about conductance. Your skin is hot and the ice is very cold so when you touch it the heat flows from your skin into the heat leaving you feeling cold.
Conductance of heat is actually quite interesting. If you imagine getting out of bed in winter, if you have a tiled floor it will feel cold but a carpeted floor will feel warmer. Even if they were at the same temperature the tile would feel colder because it has a much higher conductance.
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