Informality reigns here; jeans, sport shirts, and T-shirts fit in almost everywhere, for both men and women. The few restaurants and performing-arts events where dressier outfits are required, usually in resorts and larger cities, are the exception.
If you plan to spend much time outdoors, and certainly if you go in winter, choose clothing appropriate for cold and wet weather. Cotton clothing, including denim—although fine on warm, dry days—can be uncomfortable and even dangerous when it gets wet and when the weather's cold. A better choice is clothing made of wool or any of a number of new synthetics that provide warmth without bulk and maintain their insulating properties even when wet.
In summer you'll want shorts during the day. But because early morning and night can be cold, and high passes windy, pack a sweater and a light jacket, and perhaps also a wool cap and gloves. Try layering—a T-shirt under another shirt under a jacket—and peel off layers as you go. For walks and hikes, you'll need sturdy footwear. To take you into the wilds, boots should have thick soles and plenty of ankle support; if your shoes are new and you plan to spend much time on the trail, break them in at home. Bring a day pack for short hikes, along with a canteen or water bottle, and don't forget rain gear, a hat, sunscreen, and insect repellent.
In winter, prepare for subfreezing temperatures with good boots, warm socks and liners, thermal underwear, a well-insulated jacket, and a warm hat and mittens. Dress in layers, so you can add or remove clothes as the temperatures fluctuate.
If you attend dances and other events at Native American reservations, dress conservatively—skirts or long pants for women, long pants for men—or you may be asked to leave.
When traveling to mountain areas, remember that sunglasses and a sun hat are essential at high altitudes, even in winter; the thinner atmosphere requires sunscreen with a greater SPF than you might need at lower elevations. Bring moisturizer even if you don't normally use it. Utah's dry climate can be hard on your skin.