Science time!
So, sweating cools us down because the sweat evaporates. That requires heat, and sweat evaporating off your skin gets some of that heat from your body. Now, the air is absorbing heat from you too, but liquids transfer heat much better. That's why sweat cools you, and why moisture evaporating in general feels cold.
Glycerin and propylene are hydroscopic: they attract water to them. Your atomizer hurls out the
e-liquid in tiny bits, they attract moisture in your lungs (or just the air), which condenses and makes the visible vapor. When that touches your skin, it feels cool for the same reason sweating works, or misters work.
Cloud seeding (artificial rain-making) works the same way: spread a bunch of hydroscopic stuff in the air to get clouds to form in it.