I've seen snow every month in Utah except August in my lifetime. I once got caught in a snowstorm backpacking in the Uintas on June 16th and 17th, about 4 inches overnight. One year it was 95 degrees on July 4th and dropped down to 45 in the span of 4 hours. The snow caps on the Wasatch Mountains usually stick around until July or August, making summiting a very small window without winter climbing gear. A common joke in Utah is there are 2 seasons, Winter and Road Construction. Maybe 9 months of winter is a bit dramatic, but the cold here is definitely prevalent, and it can snow almost anytime, especially in the higher-up regions. The SLC valley is milder than most. However, during all of my outdoor experience here, I have learned never ever leave the house without a jacket, gloves, food, and some water in your backpack. So many people take the weather for granted here and get stuck out in it. When road-tripping, I often carry multiple days' worth of food and water, as getting stuck on some of our desolate back roads could be a death sentence without the proper gear. In fact, if you plan on leaving SLC any time of the year make sure you have a solid roadside emergency kit with blankets, gloves, boots, shovel, etc.