Do bring warm clothes—warmer than you think you might need. Most people are not used to being outside late at night, and you may find that it's a lot colder than you expected.
Wear sturdy footwear, such as running shoes or hiking boots. In the dark it's hard to see what's underfoot and what you might be stepping on, so your feet should be protected from sharp rocks, cacti, or whatever creatures may inhabit the ground at your site.