Typical of the Southwest, temperatures can vary considerably from sunup to sundown. Generally, you should pack for warm days and chilly nights from spring through fall, but this is a huge state with a tremendous range of elevations, so the most important thing is to check local weather conditions before you leave home and pack accordingly. In April for instance, you may need to pack for nighttime lows in the 20s and daytime highs in the 60s in Taos, but daytime highs in the 80s and nighttime lows in the 50s in Las Cruces. Any time of year pack at least a few warm outfits and a jacket; in winter pack very warm clothes—coats, parkas, and whatever else your body's thermostat and your ultimate destination dictate. Remember that Taos and Santa Fe are both at about 7,000 feet elevation and winters here may be sunny, but they are cold. Sweaters and jackets are also needed in summer at higher elevations, because though days are warm, nights can dip well below 50°F. And bring comfortable shoes; you're likely to be doing a lot of walking.
New Mexico is one of the most informal and laid-back areas of the country, which for many is part of its appeal. Probably no more than three or four restaurants in the entire state enforce a dress code, even for dinner, though men are likely to feel more comfortable wearing a jacket in the major hotel dining rooms. If you need a rule, stick to business casual and you'll feel comfortable wherever you go.
The Western look has, of course, never lost its hold on the West, though Western-style clothes now get mixed with styles from all over the globe. You can wear your boots and big belt buckles anywhere in the state, even Albuquerque, but if you come strolling through the lobby of the Eldorado Hotel looking like Hopalong Cassidy, you'll get some funny looks.
Bring skin moisturizer; even people who rarely need this elsewhere in the country can suffer from dry and itchy skin in New Mexico. Sunscreen is a necessity. And bring sunglasses to protect your eyes from the glare of lakes or ski slopes, not to mention the brightness present everywhere.