JMW Turner was a Romantic, part of the art movement that celebrated the magnificence of Nature. So when he painted Hannibal and his Army crossing the Alps in 218 BC he confined the great army and those famous elephants, to a footnote. The pride of place is given to Nature, the towering vortex of the Snow Storm.
On December 18th in 218 BC the Alpine weather was not a problem for the Romans. That was the date when the Legions met the recently arrived Hannibal. In the Battle of Trebbia he handed the Roman Republic the first of the three enormous defeats they suffered in the Italian Peninsula.
From a Roman Army of 40,000 only 10,000 survived. Tiberius Sempronius Longus was able to save his core veteran heavy infantry by forming a hollow square and retreating from the battlefield in good order. The Roman and Allied cavalry were routed by the Numidians. The Roman light infantry and the Auxiliary forces of allied Celtic tribes were driven into the river and many drowned. Any surviving Celts probably switched sides and the battle was a recruiting drive for Hannibal. The fresco below is from the Hall of Hannibal in the Capitoline Museum in Rome.