Ekaterinburg has a continental climate with cold winters and warm summers. The best time to visit for outdoor sightseeing is May through September, when temperatures are comfortable and the city's parks and riverside promenades are in use. July is warm — often 25 to 30 degrees Celsius — and the long summer days give plenty of time for walking the city. Spring arrives relatively late (April and May) and autumn is brief but golden, with the birch forests around the city turning vivid yellow in September.
Winter (November through March) is cold: temperatures regularly drop to minus 20 Celsius and occasionally further. The city operates normally through this — Russians are practical about cold — and the museums and indoor sights are as accessible as ever. The Romanov pilgrimage walk on 17 July is worth timing a visit around if you are interested in Russian history; thousands of pilgrims walk overnight from the Cathedral on the Blood to the Ganina Yama burial site.
One practical note: Ekaterinburg is two hours ahead of Moscow time (MSK+2), which affects flight and train connections.