Visitation Statistics. The park is open every day of the year. The park occasionally has to close in the winter time due to snow storms. The busiest months of the year are July and August. The second week in August is traditionally the busiest week of the entire year with as many as 3,000 people a day entering the park. Some of the slowest winter days will see less than 50 people in the park. Visitation Statistics - Mesa Verde National Park (U.S. National Park Service)