The Art of Natural Dressage

But it doesn't solve the problem, that there is something special he is lacking - since he does still search for acorns when we are in the forest.

OAK TREES - Quercus - Both the leaves and acorns of the tree are poisonous. Some horses/ponies may develop an appetite for acorns with serious consequences, however the comsuption of small amounts is probably harmless; but to be safe fence off any oak trees during the autumn.

Okay, I just thought so - since the horse knows pretty well what's dangerous to eat and not.

Oak (Quercus Spp)

Poisoning by oak is usually seasonal, being most common in spring when the young buds or leaves are eaten and the autumn when the acorns are eaten. Oak leaves and acorns contain tannic acid which is poisonous to horses and though eating a small number of leaves or acorns is almost certainly harmless, they can also be addictive, and once a horse has acquired a taste for them they can actively search them out. Also some animals seem to be more suseptible to oak poisoning than others with individual animals having different levels of tolerance.
Oak poisoning causes gastroenteritis and kidney damage.
Symptoms include:

lack of appetite
staring coat
constipation followed by diarrhoea which may be bloodstained
abdominal pain
depression
blood in urine
There is no antidote. The horse is treated with drugs to reduce the pain and control the diarrhoea, antibiotics may be prescribed.
Prevention
In general it is best to restrict the access of horses to acorns, particularly if other food is scarce,or else pick up the fallen acorns at least once a day - although this method is time-consuming and less effective as most horses will still find some. The best thing to do is fence off oak trees - either permanently or with electric fencing.