Considering that’s a Holstein breed cow and therefore a milking cow, the nutritional demands are entirely different. Getting a cow to produce 40 liters of milk a day is no easy task and requires grass of the highest quality, combined with a generous dose of concentrate feed with grains and legumes/presscake. If a normal hobby horse was fed a diet like this they would turn obese almost instantly. In fact hobby horses usually require as poor quality feed as possible because it turns out that being ridden at walking speed for an hour 1-2 times a week is a very low amount of exercise for a horse. You have to intentionally grow as rough and low quality grass as possible for the horses not to get obese. That’s why oats are no longer given to horses. A race horse or a working horse that’s active for several hours a day can however be given oats or other concentrated feed and may be able to handle, or at least come close to handling, a dairy cow type diet. However these types of hard working horses are rare nowadays.

TLDR dairy cows and horses generally do NOT eat the same diet.