Where do cold water currents begin?

if a current originates near the poles and flows towards the equator, it will be colder than all the water it meets. Hence it will be a cold current.

...conversely, if it originates near the equator and flows towards the pole, it will be warmer than the water it meets and be a warm current.

In a Short Summary Cold Ocean Currents Originate From The Poles And Warm Ocean Currents Originate From The Equator