No, platies are not cold water fish. Platies are native to southern Mexico and the east coast of Central America. Thus, they are considered tropical fish.
However, some pet shops do promote platies as cold water fish, which is simply not true. While platies are hardy and can withstand a wide range of conditions, they will not survive long in cold water tanks.
Platies require a relatively warm temperature of around 70°F to 82°F (21.1°C to 27.7°C). Anything colder than that will result in a sluggish metabolism, a weakened immune system, stress, illnesses, and eventually, death.