So using the background of the main question over here, the question over here would be, how would peasant life be like, supposing that horses are so cheap and plentiful that everyone would have a horse and the horse would need little maintenance.
Do note that the answer should also include about how people would be able to work considering the large number of horses available to them.
If there was enough horses for everyone then the poorest people would still be fairly 'rich'. This is because no matter what very few would be so poor they'd starve. A single horse could feed a very poor family for months through a harsh winter. As others pointed out (including me on a different question) study up on the Mongols especially around the time of Genghis Kahn.
Read about Genghis Khan. Nomads have plenty of horses. Peasants don't need many horses to run around, they don't need the mobility which horses provide - they are more sedentary to tend to their crops, and feeding extra horses is waste for them, or even leaving land as pasture for horses is waste. Peasants needs just few horses, and cattle.
So nomads will attack peasants at the end of growing season to steal food produced by peasants. They will harvest selectively, just like Golden Horde did: "harvesting" different peasant areas every year, returning every 10 years or so.
