Evan, as I'm sure you're aware, it depends on the weather, but it can be done in a day - around eight hours. Toas would be about an hour and a half less driving and the snow is great right now if you can fit in a day of skiing there.
That said, if it was me I'd consider leaving Steamboat around 7:30 or 8:00 a.m and driving to Buena Vista or Salida for the night. Ski Monarch for a half day. It's a great place. From Salida to Santa Fe in a little more then four hours the next day. I'm very confident you'd really enjoy this option.
I don't know how long you'll be in Santa Fe for, but if you can, get up to Taos one day while you're here. It's an easy drive from Santa Fe to ski Taos and return in one day.