Actually, some of the steppe people do use horses. They ferment mares milk into a drink called kumis, which reduces the lactose content and replaces most of it with alcohol - but most modern kumis is made with cows milk (with added sucrose, as mare's milk has more lactose than cow's milk). There's also something of a market for mare's milk - which is satisfied by a few small producers, but it's considered a luxury food.
In other words, we do not use horses for commercial milk production. Why? It's because of a peculiarity of ruminants (cattle, goats, and sheep). Ruminants will keep producing milk even after the offspring it is intended for is removed, as long as a pump is applied regularly.
Horses won't. If you take a foal away from a mare, the mare will lose her milk almost immediately. Applying a pump doesn't help. (I'll talk about the other differences between horses and ruminants over time, including explaining why we don't ride cows). So, you can only take the surplus from a mare over what her foal needs - now, mares have successfully raised two foals, so you can get quite a bit, but it's nothing like the production from cattle.
Because of this, the few horse dairies in existence are horse breeders producing the milk as a sideline. Usually draft mares are used - being larger they have larger udders - and the male foals are sold at weaning to draft horse enthusiasts. Mare's milk is primarily used in cosmetics rather than being drunk because of the large amount of lactose in it.
So, that's why we don't use horses for commercial milk production? For worldbuilding purposes, though, you may well want to have a culture that uses it to make kumis or similar. True horse people will use horses for everything - transportation, racing, meat, milk and leather.
Image: An Icelandic mare feeds her foal.