When alcohol is rubbed onto the skin, the liquid may begin at room temperature, yet the skin quickly feels cool. Alcohol is not carrying some special store of coldness. Evaporation requires energy: molecules entering the gas phase must overcome intermolecular attractions, and part of that energy is drawn from the skin. Its surface temperature therefore falls for a short time.
Ethanol or isopropyl alcohol in common antiseptic products evaporates readily at room temperature, so the change is faster and more noticeable than with the same amount of water. Moving air carries alcohol vapour away from the skin, while dry air also favours evaporation. With little airflow, or once vapour has accumulated nearby, the cooling usually weakens. The essential process is an endothermic phase change, not unusually cold alcohol before contact.
The strength of the sensation also depends on the amount used, the area covered, ambient temperature and individual sensitivity. It cannot be used to judge alcohol concentration or skin health. Alcohol is flammable, so the effect should never be demonstrated near a flame. This small experience shows that temperature can change not only when hot and cold objects touch, but also when matter changes state and exchanges energy.
https://openstax.org/books/university-physics-volume-2/pages/1-5-phase-changes
https://webbook.nist.gov/cgi/cbook.cgi?ID=C67630&Mask=4&Units=CAL
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