Do EV charging stations need coolant?

Usually not liquid coolant loops. Heat pipes and heat sinks and radiators are usually enough. They can generally put more silicon (MOSFETs and stuff) without worrying about weight as the stations are stationary. (So lower Rds values and more efficiency) Source: general EE knowledge, and owning a charging station for a Chevy Volt

Liquid loops are most useful at transferring heat rather than getting rid of them. (You still need a radiator) They are often employed to deal with high heat density applications, like processors or lasers and stuff.

Also - it's probably way cheaper to put a few more MOSFETs instead of dealing with liquid cooling. Pipes and pumps are expensive! Maintenance and repair costs would probably skyrocket with liquid cooling too. If they want to deploy these stations en mass across various harsh environments, liquid cooling is not the way to go.

I've heard that the newest 350 kW charging stations use liquid-cooled cables.