Golden Trout are extremely rare in Utah, and are only found in a select few high mountain lakes in the High Uinta Mountains. They are native to California, but even there they are not nearly as common as they used to be. If you are lucky enough to find a lake that has Golden Trout in it, you would be best to keep it to yourself, as there are only a couple lakes in the High Uintas that have them, and they all require a long hike in to remote lakes in the backcountry.
In 2012, about 13,000 one-inch golden trout were aerial stocked in the three lakes in the Atwood Creek Drainage and in 2013-2014, more than 11,000 five to six-inch golden trout were stocked in Echo Lake.
If you find that you are catching only Brook trout, try casting farther out, as the Goldens may hang out a bit farther from shore. Small flies such as #14 or #12 caddis should work great for Goldens.