Option 1: The fur of animals living in colder regions does offer some protection from water. However, this is not the primary function of their fur. The primary purpose of their fur is to provide insulation and keep them warm.

Option 2: This is the correct answer. The fur of animals living in colder regions is designed to trap air. Air is a poor conductor of heat, so when the fur traps air, it creates a layer of insulation that helps to keep the animal warm. This is crucial in colder environments where temperatures are low and the animal needs to retain as much body heat as possible.

Option 3: While the fur of animals may offer some protection against enemies, this is not the primary function of their fur in colder regions. The insulation provided by their fur is the main benefit in these environments.

Option 4: While the fur of animals may contribute to their beauty, this is not the primary purpose of their fur in colder regions. The primary purpose is to provide insulation and help the animal survive in low temperatures.

In conclusion, the fur of animals living in colder regions primarily traps air to keep them warm, not for protection against water, enemies, or appearance.