Are any jet engines used in combat aircraft water cooled?
Jet engines are cooled and temperature managed by the mass air flow itself which is used to surround and limit the boundaries of the flame, keeping it away from the burner can walls, and dilute the heat of the flame as it passes to the turbine (only a minority of the mass airflow's oxygen is actually burned - which is why afterburners work; there's lots of leftover oxygen to work with). 

If you're talking about using a closed liquid cooling system with heat exchangers taking heat from the burner can and turbine somehow, well, I've never heard of a water jacketed burner can, and how you could use liquid in a closed system to cool a turbine, who knows.  

Liquid cooling was used in the past as supplemental cooling to increase available power by spraying water directly into the mass flow as mentioned here, but in that case the water is a consumable.