The entire Sangre de Cristo range will be much too snowy in February to overnight, but you could do some shortish day hikes around Santa Fe. If you want to overnight I think your best bet is Bandelier National Monument's backcountry near Los Alamos (where I live). It is less than an hour from Santa Fe. Keep watching the weather, we are having a fairly dry winter, so much of Bandelier could be snow-free except high up the deep canyons. You will likely have to deal with temps in the teens at night and 30's to low 40's during the day though.
Santa Fe and Los Alamos are both above 7000 ft and much of northern new mexico is even higher than that so it isn't your typical desert and winter backpacking isn't often feasible without snow. Day hiking is definitely possible though, especially if you head south towards Albuquerque.
Let me know when you are coming through and maybe we can meet up for a hike.