What do the horses represent?

Horses were pressed into war service, especially towards the end of the war when the Germans were running short of oil.

Horses replaced tractors on farms and could replace (some) trucks by pulling wagons on roads, thus freeing more fuel for tanks, U-boats and aeroplanes.

Clearly dinner for some people from what we see in the film.🐭

The horses represented the more 'chivalrous, nostalgic' time in warfare: Dirty Pitt and his Dirty Tank represent a more mechanised, dehumanised and brutal conflict. Case in point with the opening- noble-looking, classical warrior on horseback gets brutally murdered by a greasy Tanker. Film ain't too subtle about these things.

In addition to all other comments, I think it's important to point out that tanks replaced horse-mounted cavalry, starting in World War 1. Due to the nature of trench warfare, cavalry troops mostly fought as infantry on foot. In the following decades, most of the major powers converted to armored cars and tanks. in WW2 some Axis powers retained horse-mounted regiments. In Korea and Vietnam, tanks were replaced by helicopters, in many aspects of combat.

If there's any symbolism to the large number of horses, it's to show the changing times. Also, Germany may have been an industrial super power like the US, but it had not undergone the huge industrial boom that the US experienced between the wars (but to rise from utter ruin in 1918 to the peak of its powers in 1939 was still very impressive), and was in many aspects like many other European nations where horse-drawn vehicles still played a big role in every day life. It's quite a contrast with the affluent USA where large distances and mass-industrialization replaced horse with train, car and truck on a much larger scale.

Have you seen Spielberg's War Horse? There's a scene where the protagonist horse, who has been a part of WW1 since the beginning in "old school" 1914 when cavalry charges were still the main tactic of mobile warfare, is confronted with a modern day tank and has to make way for the lumbering monster. There's no better, and sadder, symbolism than that.

The horse story was symbolic of the fact that the entire tank team had been fighting together since Normandy. They spent an entire day just mercy killing the horses...the job, the smell, the fact that they had survived the most grueling day they'd had thus far in their fighting...and Don (Brad Pitt) was treating Norman, the rookie, (Logan Lerman) to a nice meal...probably the first real meal they'd had in quite some time. They were pissed that he had not included them. They'd managed to survive one awful attack after another since they started fighting and he was treating the new guy like family while excluding them.