Yes, it IS early in the season, so go prepared. I'm sure you will probably get to see all the sights on the itinerary, but you need to be prepared for all kinds of weather. We were in a blizzard on the fourth of May once at the Grand Canyon! It can be snowy and cold, or lovely and warm at any of these western national parks at any time of the year.
Take long underwear! Take an umbrella. You need long pants as well as short ones, warm gloves, warm socks and sturdy broken-in shoes, a warm, water resistant jacket or a warm fleece with a water resistant windbreaker, (I used my Land's End Squall last time we were in Yellowstone in late June, for it was cold and windy and there was still plenty of snow on the ground. But on that same trip, in Cody Wyoming, I had on t-shirts and capris.) The Utah National Parks are the same way.....You never know what the weather will be like. The abundance of mountains and the altitude differences contribute to the variety of weather conditions you will encounter.
That being said, you are in for such a treat. We love the parts of America you will be seeing, and the scenery on this itinerary is spectacular. Trees and flowers will be beginning to show in many areas, and you may have a chance to see baby animals and birds. You will return home with a new appreciation for the vastness and the beauty of our country. Have a great time!