Animals have developed many types of tactile sensors. They take many forms each used for one specific purpose, the sense of touch.
All animals have whiskers. which allow them to see in the dark or out of their field of vision. The whiskers grow longer than the animal is wide so they can feel if they are walking into a space that is too narrow. They can feel an insect buzzing past them and the wisp of a breeze.
Like humans, animals use their skin as a vital touch organ. Horses can feel a fly landing on its rump. Many fish feel the vibration of the water along sensors on their sides.
Quadrupeds use their tentacles much as humans use their hands. Insects have developed antennae to feel. Some fish use barbels that are much like whiskers. Elephants use their trunks to touch and feel. Horses use their upper lip much as an elephants use their trunks. Both elephants and horses can pick up objects and unlatch gates using them.
The sense of touch is caused by pressure on the tactile receptors located near the surface of the skin. This causes a reaction to a stimulant like a summer breeze on your face which usually makes you close your eyes to better feel the sensation. When animals feel this pressure on their whiskers they react by moving away from the pressure.
The Milwaukee County Zoo has many exhibits explaining the tactile senses in animals.