In the Second Punic War, Hannibal famously pushed his troops (and ~37 war elephants) through the snowy Alps of Northern Italy.
Rome expected him to make this move.
But they did not expect it during wintertime. That is what makes this decision a brilliant (but ugly) move.
To traverse the snow and ice his forces built their own roads, blew up boulders with fire & vinegar, and faced starvation at sub-zero temperatures.
A lot of warriors died.
But, the payoff for Carthage was non-linear. After exiting the Alps Hannibal’s forces crushed the smaller armies that were stationed in Northern Italy and ravaged Rome for the next 15 years.