My high school history teacher once told me that WW1 was won by horses. Can this statement be truth if we compare horses to mechanized transport in given war?

It is a colourful, but certainly valid statement. In the case of the French artillery, 70-80% of units were reliant on horse-drawn transport, and it remained the case throughout the war that the majority of transport in the armies of the Great Powers was horse-drawn. Basil Liddel-Hart was wont to note that the tonnage of fodder shipped to France for the British Expeditionary Force during the war outnumbered the tonnage of munitions (5.9 million to 5.4). Horses towed guns, supply wagons, and ambulances, provided mounts for the dispatch riders and mounted MPs in the rear areas of armies, and were the source of mobility for the Cavalry of the armies. They were an essential part of the First World War and also of the Second, while their role was definitely both heroic and tragic, not unlike their human companions in that respect.