Maybe you are from Florida and do not know cold, but even if you do, you cannot imagine the misery a winter campaign brings.
It’s cold. I do not mean “Oh, I have to go from the parking lot to the office at 20°F”. I mean spending 18 hours a day in freezing temperatures without any shelter. Your body continuously leaks energy and you will feel colder and colder by the hour. You will feel numb, maybe weak. You might start to shiver uncontrollably. You might drop your musket, when you stop feeling your hands. But that is not even actual freezing yet. And to top it off, in the evening you will then not go into a house to thoroughly warm yourself, but you will sit around a campfire, only to repeat the experience day after day for weeks. This does not just lower morale. Low temperature will easily cripple (frostbite) or kill your soldiers. Most armies did not hand out adequate winter clothes, so the soldiers suffered.
There is less food. In summer, you might find ripe crops, farm animals you can slaughter, general vegetation for your animals, … In winter, all of this has been harvested and the grass or bark your horses need to sustain themselves is covered by snow or frozen. And your troops are distracted by the need to gather firewood in addition to food. And as your horses are in bad shape/dead due to less fodder, your foraging parties will have a very hard time trying to bring back adequate amounts.
Mobility is a diminished. Snow makes roads much harder to travel (e.g. you have to wade through knee-deep snow), your horses and men will slip on ice/stumble across roots and break ankles, soldiers are unwilling to leave houses, … Once the snow melts, the cumulative water turns every road into a big pool of mud and rivers flood the countryside.
Less daylight. That might not seem like much, but in an age before electric lights, natural light was an important resource.
One of the most famous defeats in history, Napoleon’s Russian campaign, was crippled by winter (although winter was not the only thing that defeated him). Based on the book “1812”, here are a few extra examples of things the French were suffering from:
Frostbite. Once all of your toes have fallen off, you cannot walk anymore, because you cannot keep your balance. If you lose all your finger, you cannot use muskets. Neither can you feed yourself without aid. To make matters worse, many of Napoleon’s soldiers were from southern France, Italy, … and simply did not know how to deal with frostbite (or the harsh winter in general).
Inadequate uniforms. The Grande Armee quickly became barbarized as soldiers covered their fancy uniforms with every scrap of cloth and fur they could find.
Incompetent officers. Some officers forced soldiers to parade in freezing temperatures. E.g., when the retreating French reached Vilnius, the commander of the city sent his troops to greet them. They wore normal uniforms and died within hours. The French army had to limp the last miles to the town past the corpses of 8000 young Frenchmen sent into death.
Sometimes it was so cold that when French soldiers touched to metal of their muskets, their skin froze shut and they had to rip their hand off, leaving the skin. Now try to imagine reloading a muzzleloader with thick gloves on
Hi, you may be interested in a few more responses here, which focus on the campaign season in Ancient Rome