When would be the best time to xeriscape in Colorado Springs?

Check your county or state university Extension service. Google agricultural extension service, with your town and zip code.

Contact them and they will happily suggest when and what native plants would be best for your soil and weather.

I would think any time would be great, as long as it is not to chilly for you on the day to begin to work. Friends in arrid Calif. and also AZ have been doing it now. You have more options for time than folks in northern Colorado, as your weather is milder. You may want to wait on a few succulents until the weather is warmer, but some are ok even now like chicks/hens or prickly pear. Here are some ideas for you: https://www.hometalk.com/diy/outdoor/garden/beautiful-yard-even-in-harsh-dry-deserts-39160211

Beautiful Yard Even in Harsh Dry Deserts!