Yes, I've dyed sheep, Cotswolds that is, with Kool Aid for our county fair, for the Spinner's Jamboree. Here's how: Take one very friendly tame sheep, who will hate you for this, wash in cold water with a hair shampoo for greasy, oily, dirty, hair. (Use a people shampoo!)  Rinse well, wash once more with shampoo. Don't use too much as the first time it won't suds too well, and the second soaping just use a little as you will rinse forever if you use too much. Then let sheep dry, help with towels, if she is still speaking to you by this time. (a hot day helps, too). Then mix whatever color of Kool aid as follows: 2 packages of cool aid to 1 c. of cold white vinegar.  Pour on sheep and rub in with hands. If you don't want your hands dyed, use rubber or latex gloves and very old clothes, because the sheep will manage to shake just like a dog and get the dye all over your clothes. It will take several packages to dye one Cotswold adult ewe with a six inch staple length. I use several colors and make a rainbow sheep. Also, to get a bright yellow or green, I use food coloring, as Kool-Aid doesn't make those two colors. Next, let sheep dry overnight, and then rinse very well, with lots of cold water. The excess dye will rinse out. The sheep will have a fruity smell with a dash of vinegar. The dye job is pretty color fast, as I have spun the wool and washed and set it and the color remains. Now, I have also asked my vet, who's a sheep and goat specialist, and she said this does not harm the sheep in any physical way. I also make sure that the sheep has a very clean and draft free place to stay till dry and time to go to the sheep to shawl.  I don't dye the sheep until a few days before the contest as I want the sheep to be as clean as possible for the shearing.  

The best breeds of sheep for Kool Aid dyeing or food coloring dyeing are the long wool breeds as they tend dry faster and not mat up like the finer wools.  Since I raise Cotswolds, that is what I have dyed for sheep to shawl contests, but Romney, Wensleydales, Border Leicester, and Lincoln sheep to name a few would all be great for dyeing.  It gives some color to the contest and we shear the sheep right before the contest begins and it does certainly draw a crowd to watch the start of the sheep to shawl contest.

Please let me know if you enjoyed this guide.  It was meant to be humorous while actually telling you how to dye a sheep for a spinning competition.