Although lowering humidity can be more easily done with just ventilation.
Mandatory slightly related anecdote: on a summer drive through Morocco back when car air conditioners where a thing exclusive to America and the one percent I never felt sweaty as long as the car was moving.
(I live in a dry climate and generally don’t sweat much anyways, YMMV)
I have an ice vest if I really want to go outside for then a few minutes.
Mirror clothing sounds like a dream.
And when they are used outside, the added humidity is negligible compared to volume of surrounding air.
Your intuition about temperature is focused on the dry-bulb temperature that a simple probe gives you.
A wet-bulb is literally a probe with a wet cloth or tissue around it.
As the humidity in the air increases the wet-bulb temperature approaches the dry bulb temperature.
This is absolutely “warming”. The latent heat of the air increases. The sensible heat remains the same.
Edit: to be clear I am not suggesting heat/energy disappears. In this case they are cooling the air and the body using evaporation. The system appears to suck in hot air on one side and ejects cooler humid air on the other. More or less human swamp coolers.
https://en.m.wikipedia.org/wiki/Evaporative_cooler#Physical_...