Despite a rough early season of snow clearing (resulting in the breakdown of two bulldozers), Yellowstone National Park officials have been working throughout the spring in an effort to clear the roads and open the park to vehicle traffic. The Park's South Entrance is scheduled to open today, May 9th.
However, with the snow being a little unrelenting this spring, it's certainly worth giving the National Park Service a call to get updated information regarding current park closures, regulations and infromation.