Lots of things influence the temperature of the water in a river. The local ground temperature is an important consideration. Or the river may come from ice melting in the mountains. At certain times of the day, the temperature of the air may drop quickly and the river temperature will be warmer than the air. For an entire winter season the air temperature might remain below the freezing temperature of water while a flowing river remains ice free.
But let us not argue with the question too much. Open water will lose heat to the air as it evaporates. That is, faster molecules in the water will tend to leave through the surface and become a gas (water vapor). This leaves behind the slower, colder, molecules.