Hi Tatyana. Your English is fine. In fact I have noticed that Russian speakers do better English than most people.
As I said before I'm really not an ASB person, but I'll try to help.
Climate? I'd treat an ASB like a thoroughbred race horse. Lots of good food (grain and hay), shelter from the wind, and good blankets. I think you would have to keep them in a stall during the coldest, windiest weather. The ASB is not very feed efficient, I would be prepared to feed them more than an equivalent sized horse of other breeds.
The beautiful high airy action is bred in, watching a loose ASB can be exciting, with fluid, high and airy action at the trot. To make this natural action higher the show people try to grow the hoof out as much as they can (up to 10 cm longer than normal) and I think they pack weights into this extra hoof space. They also sometimes train with a device that uses elastic tubing attached to the horse's pastern which goes up to the surcingle (schooling girth) while lunging the horse. They also hold the horse's heads WAY UP and flexed at the poll when riding or driving.
The tail is not natural. The veterinarian cuts the two depressor (holding down) tendons of the tail, them the tail is kept in a tail set when the horse is not ridden. The show horses are never turned out to run around, so the tail set stays on and so that the extra long hooves don't break. The ASB carries an unset tail a bit higher than most breeds but not as much as an Arab.
Have you tried these web sites--http://www.ahsa.net, or http://www.american-saddlebred.com ?
We were lucky in America, when the Europeans basically threw their gaited breeds away we already had the gaited blood in the Americas, South and Central America have their Paso breeds, and in America we have the ASB, Tennessee Walker, Standardbred, and Rocky Mountain horse and possibly others, all with easy gaits for riding.
The older ASB people back in the early 1900's onward just did not think that a

Hi Tatyana! Do you get to ride in Russia very much? You say it is not as common as in Germany and the rest of Europe, but are there still riding schools in Russia?

 

Paco is actually my pet fish! I do not have any horses at this time :( I am going to university in September, and hope to start riding again at that time.

Welcome to Barnmice, Tatyana! :) American Saddlebreds are beautiful animals! One of my close friends has an American Saddlebred, and she is one of the greatest horses I've come across.