Evanston sits at 2,100 metres elevation, which means cold winters and warm summers. June through September is the most comfortable period for outdoor activity — Bear River State Park and the Uinta Mountains are accessible, and temperatures are pleasant during the day, though nights can still be cool.
Winter brings snow from November through March. The Uintas get enough snow for snowmobiling and cross-country skiing, and the park trail is open to snowshoers. If you are coming primarily for the Bear River bison herd, winter is actually a good time — the herd is more concentrated and easier to spot against the snow.
Spring (April-May) is variable: the higher Uinta trails may still be snow-covered, but the valley is green and the rivers run high with snowmelt.