I'm pretty sure you already know the answer to this, but for the sake of discussion here you go.

There are several parts to this answer, and I don't claim to know them all. Also, not a scientist, so take my answer for what you will.

Moving water is mixing water, and has higher kinetic and internal energy. Yes, "friction" does occur among the H2O molecules, but plays a smaller part in keeping the water from freezing than the mixing with warmer water. Water freezes by convection to the air due to the presence of temperature gradient. Water is cooled by colder air. The colder the air, the larger the gradient, the quicker this occurs. If the water is not moving the surface molecules will be in constant contact with the air and will cool and freeze (stop moving) more quickly. But with moving water the molecules that were on the surface a second ago cooling towards freezing, are now being mixed with warmer molecules below the surface slowing if not mostly undoing the cooling that had occurred from the convection from the air.

Like I said, there is more to it than that, but mixing and "interrupting" the convection occurring is the greatest reason moving water doesn't freeze.

Ryan