Weather. In a nutshell, bad weather makes battles harder. This is because walking a long way while wet sucks, it damages supplies and equipment, it increases the likelihood of disease, and there are intermittent dangers like flooding that are hard to predict in unfamiliar territory. In general, people know how to manage these things where they live, so the worse the weather, the bigger an advantage for the defender (or at least whoever marched less).
How does battle outcome relate to barometric pressure, and the movement of air pretty high up?
Weather. In a nutshell, bad weather makes battles harder. This is because walking a long way while wet sucks, it damages supplies and equipment, it increases the likelihood of disease, and there are intermittent dangers like flooding that are hard to predict in unfamiliar territory. In general, people know how to manage these things where they live, so the worse the weather, the bigger an advantage for the defender (or at least whoever marched less).