Thank you for the information and the picture! :)
I am glad you did not find any nits on the tape-so lice is out! I am not convinced that it would be mange either since she is not itchy at all. Typically mange is extremely itchy and you would notice her rubbing everywhere!
I am concerned about possible infection from moisture on the skin or possibly ringworm. Since she is mainly in a stall, is young, and it is spring time (less sunshine), ringworm is a good possibility. It too can be itchy, but not always. Most symptoms you see are fur loss present in irregular areas across the body.
A few different things you can do to treat it: 1) get her out in the sunshine more (which can be challenging if it is as gloomy and rainy where you are as it is here in Ohio!), 2) betadine or iodine scrub (use a toothbrush to scrub the areas once a day for 7-10 days), 3) topical antifungal such as lotrimin, daily for a week, or 4) a topical antifungal from your vet. Make sure you wash your hands afterwards as you can get ringworm too!
Now it will take a good three weeks for any fur to begin regrowing! :)
Hope this helps! Please let me know if you have any further questions!!