refrigerant boils at a low temperature and cools the evaporator coil and then a fan blows across it to cool the room

but what is happening on an atomic scale? if "lack of movement" is all cold is, how does cold air blow in my face?

uhhh

here's a very new video explaining it

Simply put, the movement of the molecules, or the heat, transfer from your face into the air surrounding you, since the air blowing in your face has less heat in it (lower temperature).

The heat equation and Fick's second law explain the pattern, where heat flows from an area of high concentration to an area of low concentration.
https://en.wikipedia.org/wiki/Heat_equation
https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion#Fick.27s_second_law

Because heat is motion of particles, heat flows from hot to cold through collisions on the microscopic scale.
Heat flows from you to the cooled air in the same way that it flows from the air to an ice cube thus causing it to melt.

The reason for this is that the particles from the more heated material collide with the ones in the less heated material, thus transferring energy to them and causing them to move faster.

It sucks the energy from the air around you. But who needs energy when you can feel comfortable.

It doesn't, or if you can prove that it does - I'm going with magic.

this was the greatest video I ever watched

Heat is average kinetic energy. Your face molecules are vibrating in a way that gives them more evegy than the surrounding air, so even though the air is moving it has less energy than your face. So once it contacts your face it absorbs energy and you get colder.

Like a bike pump connected to a spray can epic video.