Like most places, S.F.'s weather can be unpredictable, but generally, around Thanksgiving, a good chance of beautiful, cool sunny weather, and like the others said, definitely chilly if not flat out cold at night and early A.M. ( avg. highs and lows of about 50, and low 20's). But I can't think of a bad time to visit Santa Fe, even midwinter is beautiful, just very cold at night... Labor Day weekend is Fiestas weekend(oops, just checked; Labor Day is the 6th and burning of Zozobra the 9th...
http://www.santafenm.info/fiesta.htm, so possible you'll miss the fiesta crowds on Labor Day weekend). Thanksgiving while colder, will still probably be mellower, and that'd be my choice. By the way, I assume you're aware that the elevation, (in town, not the mountains,) is 7 thousand feet, so be prepared to be a little winded walking around especially the first day ( might not happen, but certainly possible). For this same reason, the nights are usually already getting at least a little chilly even by Labor Day( avg highs of about 80 , down to about 50 at night). I know some people think it's gotten too touristy, but I still think it's a beautiful, magical place after well over 30 years in NM. Whichever you decide... enjoy NM... I know you will.
(SANTA FE 2 Weather station, 5.21 miles from Santa Fe)
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual
Max °F 43.0 48.8 56.2 64.2 73.1 83.0 85.6 82.9 76.8 66.3 52.4 43.7 64.7
Mean °F 29.3 34.8 41.0 47.9 56.6 66.0 69.8 67.8 61.5 50.8 38.0 29.8 49.4
Min °F 15.5 20.8 25.8 31.6 40.1 48.9 53.9 52.7 46.1 35.2 23.6 15.9 34.2