Visiting the Holy Mountain - Tianmen Shan you will need a full day. Your first thing to do is to obtain tickets for the cable car.
Regarding the weather and the crowds April, September, October, and early November are the best months to visit the "Heaven's Gate". Be prepared for showers, but if you are lucky you can get sunshine as well.
Avoiding the Crowds
Expect a busy holy mountain throughout the year except for winter (mid-November/December - February). The main season is from May until October with most visitors and rates at its peak. Heaviest crowds in July/August. A sweet spot month with mild climate but without heavy crowds is early-November until mid-November. Otherwise, March/April are considered months without massive crowds.