One January visit to the ranger station on the rim had 3 or 4 inches of snow, but it certainly wasn't snowed in. Visitation peaks in March with Spring break when it is busy and abused. Late summer and early Fall are the next peak. The heat in the heart of summer is more than most can bear, especially with scarce water. The attractions are deep sandstone canyons with many ruins and rock art sites.
Some areas have a day use fee as well.
A reservation system is likely in 1999 to limit the number of visitors at any one time to preserve the quality of the sites and ensure a pleasant experience for visitors. National Geographic had a brief discussion of the area with an impressive areial photo in a 1996 issue.