UPDATE: 3:10p.m. Wed 23 Dec 2009
The situation has changed somewhat as the upper low is coming in a bit further south. This boosts the snowfall potential especially over the northern half of Texoma (as mentioned in the first discussion from Monday). Since this system will tend to "wobble" about a bit, snowfall is also possible ion the Texas side of the river, but in general the chances for significant snowcover will increase as you move northward. Near blizzard conditions are possible in the Tulsa area, and possibly Oklahoma City as well, Thursday.
UPDATE: Tuesday 22 Dec 2009 / 3:30p.m.
The storm system is coming together about as expected, although the trends are to take the core of the upper low further north. This reduces the chances for snow in Texoma, but experience tells me it's too soon to write off a chance of snow, at least over portions of the area, Thursday.
Since the trends suggest drier air will have wrapped in behind the front before it's cold enough for snow, I'd peg the chances of accumulating snowfall for Texoma at only 20%. Stay tuned for updates! (see rest of discussion below from Monday)