Ice is so cold if you touch it with skin because your body secretes tiny amounts of sweat, which is a salty fluid onto your skin surface it actually makes your skin stickier. It’s for grip. If you then touch that onto a very cold ice surface the ice then re-freezes the liquid on your finger. Because that liquid is a fluid and it has got into all the nooks and crannies on your finger it then freezes solid and will form a very tight bond between your finger and the ice. You get stuck to the surface. If it’s an ice cube – if it’s okay because there’s enough heat flowing through your fingers then you can detach yourself. People in the Antarctic have to be very careful about this kind of thing. It doesn’t warm up and they can end up permanently frozen to the surface.

Another explanation:

When your warm fingers touch the ice they melt its surface layer. Then heat from this newly melted ice flows into the middle of the ice cube, lowering the temperature of the outside layer enough to re-freeze it. So, your fingers melt a little bit of ice and then the ice re-freezes that layer. After the ice is out of the freezer for a few seconds its surface is warmed by the warm air, causing it to melt and unstick it from your fingers.

This re-freezing effect can also freeze the surface of your fingers – this is called frostbite. Frostbite can also be caused by low air temperatures, and causes the fluids in the body tissues and cellular spaces freeze and crystallize. This can cause damage to the blood vessels and result in blood clotting and lack of oxygen to the affected area.