Also known as just Dons, Donskaya, Russian Horse, and
русская верховая . That last one will be helpful for you if you want to find Russian websites (make sure your search engine filters allow for websites of other languages to pop up). Trust me, when you're researching 'rare' or otherwise hard to find breeds in the States, your best bet will be finding breeder websites or, better yet, breeding associations and pedigree databases, from the horse's original country.
Originally, I tried Don and Russian Don, and nothing helpful was coming up. You don't realize how annoying Pinterest is until it's the only thing that comes up in response to your searches, with pictures of all these beautiful horses of the breed you need, but no links to where they originally came from.
It wasn't until I tried Donskaya that I found it. http://millionhorse.com/russian_donskaya-horses-for-sale-breed.html
Only two, and not much information on the pedigrees. However, under Idriya's, I found a very short pedigree, only her sire and dam listed, in original Russian language, thankfully. I copied Дурман and put it into Google as 'Дурман horse'.
The VERY first link was this: http://www.rw-base.ru/horse.php?id=632 . A pedigree database! Am I good, or what? ;)
Now, here's what you need to know. If you're not using Google Chrome, I HIGHLY suggest it. Whenever it senses a language not in English, it creates a notice at the top asking if I'd like to translate. Sometimes I say yes, other times I don't, as I'm looking for key words in Russian. If at any time you want to translate the page, all you have to do is right click-- an option for Translate to English appears.
Once I translated, a whole bunch of information popped up. 'Datura' as he's translated in English, is an odd one, as bay is typically represented by a different word that translates as bay, not Kari. Also, with Chrome, if you hover over a word, the original translation appears. You can use this to copy characters that aren't on your typical keyboard, such as one of their names into the search bar. This site provides little camera icons whenever a horse has a photo. If you click just the icon, the photo will appear without taking you to the horse's page. This is handy if you're just trying to find a specific color. At the very bottom, you can Show List and an expanded list of offspring shows up. Handy!
Just so you know, gray and chestnut do not appear very often in the breed. I spent a lot of extra time tracking down chestnuts, and I think I found one gray in all that time, too. If you're interested, chestnut is рыж 'red haired' or рыжая 'red'. (Don't search this in google with your safe search off, just fyi!).
However, try searching рыжая жеребец русская верховая . I found a lot of black horses in the images, but also several chestnuts, which led me to some breeder websites, however those take a lot more time than scanning through pedigree databases. BUT, if you're clever like me, you find this - http://kskatlantis.ru/publ/razvedenie_loshadej/nashi_zherebcy/tiam/12-1-0-11 . And that 'pedigree' link on his page takes you here: http://base.ruhorses.ru/horses/pedigree.php?code_horse=969833 .
That site is quite a bit harder to use; I couldn't figure out how to let it narrow down to only the Don horses. What I ended up doing was copying names of the horses I was interested in into rw-bases' seach page.
Oh, another note, if you hit the About the Project button on hte rw-bases' page, at the bottom, it will tell you all the acronyms the site uses for the different breeds. The Russian Horse had a lot of outside influences, so don't be surprised to find Arabian, Thoroughbred, Trakehner, or Akhal-Teke horses back in some of the pedigrees.
Colors:
Black- вороная
Bay- гнедая
Chestnut- рыжая
Good hunting!