Water fountains were not equipped with cooling systems before electricity. They were simply steel, brass, and porcelain fixtures that had a valve that allowed water to flow into the air for a short distance.
This type of fountain is often found in state parks or roadside rest areas in less-populated areas.
Large fountains in public areas or cities need to be able to reach the desired height. This water pressure can be achieved by having water flow from an elevated water tower, or another storage basin. Pumps wouldn’t be required. The only problem is that the water cannot be recirculated. It would instead be sent down a storm drain after filling any catch basin it had.
A water pump can be made from a steam engine, or any other type of mechanical engine. It does not require electricity that was not produced by the engine. A pump powered by water at a lower level can be used to lift water to higher heights. A water-powered pump fills a cylindrical with a large piston. The piston is gradually pushed down by the water’s weight. An arm connects to the piston and a smaller piston acts as a pump. The large piston’s diameter moves down, and the smaller piston presses water at a lower pressure. This allows water to flow many feet higher to fill a catch basin or water tower.
Humans are very clever and have many ways to achieve things that can be done with electricity. You could also use a water wheel to transport water upwards, provided that the water being sent was not larger than the water powering the wheel. Both cases have the mechanical advantage of using different sizes. The water being sent up is smaller than the water powering the pump, while the water going up is larger. Wind power has been used for decades to pump underground water, often up to 50 to 100 feet. This same technology can transport water from ground to water tanks, which provide water at sufficient pressure to permit fountains to spray water.