I will be recieving some eggs in the near future and hope to start a good sized breeding population (they are legal in all states except AZ). I would like to try keeping them outside as a lot of fish seem to do better that way. I am curious if they are cold tolerant enough to survive year round here in southeast TN or if they would need to be brought in for winter.

I was not able to find the value for C. eremus specifically, but related species and populations of desert pupfishes had thermal minima in the range of 4.4-7 celsius (roughly 40-45 fahrenheit). They would likely need to be brought in for winter unless the water garden is heated; in any event, I would recommend heating the water garden because the day-night temperature swings play havoc on any plants you may wind up keeping with the pupfish (hardy water lilies, for example, go dormant at water temps below 60, and other water lily varieties go dormant below 70...very few areas outside of the tropics do not regularly get nighttime temps lower than those values, even in summer. This thwarted many of my prior attempts at growing water lilies...this year I heated my water garden, and it's doing far better than any of its predescessors).