The further downstream you go the warmer it gets. The Colorado below Glenwood Springs may be a good place for getting on the water sooner, then you can go out to Grand Junction or Moab for even warmer weather.
I've run Glenwood to South Canyon in January before. Wherever you go, if its before March be wary of any continually shaded places as that's where the ice dams develop. Think low altitude and open terrain. Or Mexico.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse