The low kinetic energy of it's constituent molecules seems a good guess. The temperature of any object is, in fact, a measure of the thermal energy of the atoms or molecules that make it up. This can be calculated using E=kT where k=boltzmann constant and T-=temperature in Kelvin. This is, of course, an apporximation - for a diatomic ideal gas the fugure is 3/2kT, for one with three molecules it is 5/2kT etc. but when talking about liquids or solids kT is an acceptable approximation So if each molecule in the river had relatively low kinetic energy, we would feel it as cold and transfer the kinetic energy of our molecules to the river's.
When you get out of the cold river it will feel even colder as the water molecules with high energies will evaporate from your body leaving only those with low energy.
Originally posted by D Mullholand it was surprised that a guy was thinking about a river while walking on to the sea and throwing his clothes off... :zombie: