The vast majority of the force assembled to invade the Soviet Union marched in on foot, just the same as the Roman legions did two thousand years ago. There were quite a lot of horses -at least 625,000-, but for an invasion force of nearly four million men, that doesn't go very far. A modern army needs vast quantities of supplies -about 500 tons per day per division-, and those supplies have to be pulled by cart, and the horses pulling the carts need supplies of their own, which have to be pulled by cart. Since the German carts were made of steel, and were probably more engineered than they needed to be, this supply system placed great strain on their horses.

Beyond that, the Germans rolled into the Soviet Union lugging about 7,000 pieces of artillery, most of it horse drawn, with a paper strength of about 110 horses for every four gun battery. There was very little chance for a soldier to ride a horse for personal transport, given the demands for draft horses; while a non motorized infantry division's supplies and artillery might be horse drawn, the infantry themselves usually had to walk.

Aside from horses, rail transportation formed the backbone of the Ostheer's logistical net, and ominously for the campaign, it ran into serious problems. While planning for the operation, the German logisticians immediately had to confront the fact that they just didn't have all the cars and engines they needed to move the weight of supplies they'd need to. To circumvent this obstacle, they built in the assumption that they would capture large amounts of Soviet rolling stock. When the rubber hit the road, though, the Soviets successfully evacuated much of it, certainly enough to throw of the Germans' plans to alleviate their supply situation. They also ran into the unexpected problem of Soviet scorched earth strategy. While they knew that Russian rails were wider than theirs, and made preparations to convert them fairly rapidly, it was impossible to run the trains very far into occupied territory in the first months of the war because the Soviets had demolished most of the water towers. Trains run on steam engines, and to keep a steam engine running, you need water.

In general, the preference of the German army was to move troops by train whenever possible, since it was quick and efficient, but once you reached the end of the railway, you were probably on foot for the foreseeable future.

Check out the chapter on logistics in Inside Hitler's High Command and Mechanized Juggernaut or Military Anachronism? Horses and the German Army of World War II