The number of horses in the Russian Empire peaked in in 1913 and was around 35 million in 1916 (the US had about 20 million horses in 1915, and the two countries accounted for half the global equine population). At the time, they were almost all used in agriculture.
The Soviet horse population plummeted during the Civil War, recovered during the NEP, then plummeted again during the early 1930s famine, recovered slightly again, but was further depleted by WW2, and stood at 12.8 million around 1950. The USSR then embarked on large-scale tractorization, and the horse population fell into long-term decline, reaching 9.9 million in 1960, 6.3 million in 1970 (of which 3.2 million in the RSFSR), and 5.6 million in 1980 (of which 2.5 million were in the RSFSR). It then seems to have stabilized; at any rate, the RSFSR horse population stood at 2.6 million by 1990.
Then it collapsed again in the upheaval of the 1990s, but bottomed out during the 2000s, and there were 1,381,300 horses in Russia as of 2016, the latest year for which data is available.
Where hither for Russian horses?
The US example might be instructive. The horse population peaked around 27 million in 1920, but then came tractorization, and the US horse population started plummeting due to economic obsolescence. They reached a trough of close to 3 million by the 1960s. However, people got richer, and interest in horses revived, this time for recreational reasons. By the 2000s, the horse population had gone back up to 10 million.
There are tentative signs that this is happening in Russia. While the number of horses belonging to agricultural organizations has plummeted from 2.3 million (i.e. almost all of them) to 300,000 by 2016, the numbers belonging to farmers and individual entrepreneurs has increased from a few 10,000′s in the 1990s to 369,000 by 2016.
If disposable incomes continue to increase, it is probable that the Russian horse population will become predominantly recreational, and will drive a recovery in numbers to 2-3 millions.