Here's an enclosure I did for Burmese Stars. I have humidity frequently in the teens here outside. I would set up redfoot tortoises in a similar setup. Lots of plants, use shade properly and sprinklers that can be turned on for 1 minute 3-5 times per day.
All tortoise benefit from humidity and they find it by digging or by finding plants and other cover. Growing plants creates an environment that holds humidity very well near the roots and under the fronds if you keep the plant healthy. I use Society garlic and rosemary and sturdy plants that are safe food, but tortoises don't like and eat. Grape vines to cover a fence along one side. Laventera and Rose of Sharon that grow well and drop lots of edible blooms most all of the warmer months and can survive the cold months. Grass is a great humidifier as well and a great substrate for a tortoise.
Look over this post I did for ideas. I even added a how to build towards the end of the thread...
I just about have this enclosure ready for the tortoises. I had a limited amount of space to use for my group of Burmese Stars, and wanted to take advantage of all the space I could since I was now using the last space I had for my weed garden and tortoise food it provided. Brenda is pleased...
I use overhead spray heads in my outdoor enclosure in Florida.
But something a lot less elaborate can work like a sprinkler screwed onto a garden hose.
Have lots of plants and shade like has already been mentioned.
I pounded in a line of T-posts along the middle of the enclosure space, then hung drip pipe off the tops of the posts. Every 5' I punched in drip emitters that put out a three or four foot fine mist spray. I run this daily during the summer. Also, the enclosure is deeply planted in trees and shrubs.