Q:

How can a strong water current be cold

This is a layman question.
If heat is the motion of atoms, how can a fast moving water current be cold?

A:

The  motion of molecules that is responsible for heat content in water is random motion; that is  there are molecules moving in all directions. The directed motion that you are considering ( all molecules moving in the same direction)  from the flowing water does possess kinetic energy, but it is not heat energy.
However, if the water flow  encountered some obstacle that impeded the flow and randomized the motion of the molecules, some heating would occur. In that case some of the kinetic energy of the flow would be converted to heat energy ( internal energy) of the water.
It may be worth noting though that the average magnitude of the random velocities of the individual water molecules is quite high (probably on the order of 500-600 m/sec for room temp water ) compared to the likely velocity of any "fast moving water current", so the heat energy or internal energy would be large compared to the kinetic energy of the water current as well. Thus, not much heating would be expected from  converting the flow to randomized motion.

