In this context the German concept of widespread use of horses actually was a good idea as it gave a certain logistic capacity independent of fuel and mechanics and utilised an available source of horses, fodder and men capable of handling both.
The major part of the German logistic capacity still was truck based, but without the horses the Wehrmacht would only have been able to field a fraction of its OTL force, and on the narrow track to the front unit a cart drawn by (small ugly) horses often was much more handy than a truck.
Horses are far more labor intensive, and other costs.
Like when the US was pre-mechanized, before Steam Traction engines, about 1/3 of a Farms acreage was set aside for growing fodder.
WWI showed a huge amount of transport was set aside for delivery of that low density, high bulk cargo. High numbers of horses preclude grazing, fodder and water must be shipped in.
Besides food, had to provide clean drinking water. Figure on one horse having the logistics footprint of 10 men.
Then add on that unlike vehicles, Horses need that food and water every day, if they are doing work or not.
Trucks only need fuel when doing work, and nothing when idle, and trucks required far less daily maintenance. Recall the saying,
'Rode Hard and put away wet' thats how you kill horses.
It's false economy. Horses have no place in front line operations in the 20th Century.