All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If the coolers at the mosque are endowed to the prayer performers, then it isn`t permissible for anyone else to drink from them since it isn`t permissible to dispose of the water endowed for drinking against the purpose for which it was endowed in the first place. Accordingly, not observing that purpose is an act of transgression for which a person will be held to account on the Day of Judgement.
Ibn Hajar (May Allah have mercy on him) was once asked about the water endowed at mosques for purposes of ritual purity. Is it permissible for a person to move that water to their house to use it for ritual purity although people, at the mosque, are in need for it? Is it permissible (or not) if people weren`t in need for it? He replied: "One who has donated water or has endowed items to a certain mosque to be used to achieve ritual purity isn`t allowed to move that water or those items anywhere else to be used for that same purpose. This is because it isn`t permissible to move drinking water endowed to the mosque anywhere else."{Al-Fatawa Al-Fiqhia Al-Kobra, vol.3/pp.266}. And Allah Knows Best.