How does Aloe Vera leave a cool feeling on your skin? Why does it evaporate fast?
The leaf of aloe vera is composed of three layers: 1) An inner clear gel that contains 99% water and rest is made of glucomannans, amino acids, lipids, sterols and vitamins. 2) The middle layer of latex which is the bitter yellow sap and contains anthraquinones and glycosides. 3) The outer thick layer of 15–20 cells called as rind which has protective function and synthesizes carbohydrates and proteins. So overally , it consists of about 99% water and remaining are vitamins, enzymes, minerals, sugars, lignin, saponins,etc.

So what makes inner layer gelly ?? Well, the innermost part of the leaf is a clear, soft, moist and slippery tissue that consists of large thin-walled parenchyma cells in which water is held in the form of a viscous mucilage consiting of cellulose, hemicellulos and acetylated mannans.

As for you question, as most of it consists of water(99%) the cool feeling might has been felt due to its evaporation but some of its remaining constituents are absorbed in the skin. Mucopolysaccharides present in it help in binding moisture into the skin.Its one of the important medical applications is that it could potentially be used as a
penetration enhancement agent for the transdermal delivery of drugs and intestinal absorption of coadministerd drug.link

Saponins that are the soapy substances are found in the gel of aloe vera and have cleansing and antiseptic properties link so you can say that hand sanitizer and aloe vera are somewhat connected.