Why do we feel hot and cold sensations?

It's a survival mechanism.

Extreme heat, e.g. fire, and extreme cold, e.g. ice, can be fatal to humans. So nature has equipped us to feel sensations, ranging from discomfort to pain depending on the intensity of the heat or cold, in order to warn us of the potential threat.

People who have impaired sensitivity in their fingers or toes (maybe due to a medical problem like Diabetes) have to be very careful because they are at greater risk of burns as they cannot feel when things become hot.