White River, Utah. Utah’s remote White River lies in the Uinta Basin region of eastern Utah where it drains into the Green River south of the town of Ouray. With its headwaters in the Flat Tops Wilderness of White River National Forest in western Colorado, the White River is surrounded by a sea of oil & gas drill rigs in this resource-rich area south of Vernal. Few people float the White River each year, due to its lack of significant rapids, its remote location, and its short season. The river’s flow normally peaks for a couple weeks in late May and early June as the snow in the high country melts.