The first reason for a campaign season was farmers. With large numbers of men gone who will do the planting? how about the harvesting? You needed to let your own people go home in spring and fall to ensure a continuous food supply.

The second reason for a campaign season is precipitation. Rome's weather and Climate High precipitation makes mud, floods rivers, ruins equipment. The campaign season was situated during the lowest precipitation months. The French at Agincourt tried to move heavy infantry through mud. It didn't go well for them. Carts can't move supplies because they are stuck in mud. Tiny streams that are easily hopped over in Summer are raging rivers swollen with rain requiring bridges to cross in spring and fall. Iron weapons need to be covered to keep out the rain bread and grain spoil when wet. It's very difficult to move troops through rain/snow/sleet. Marching troops on ice is amusing to watch but not particularly fun to participate in.

Ancient armies including the Romans were largely dependent on foraging for food. Even if your troops are supplied by wagon the horses or oxen pulling those wagons need food. In summer the animals can be allowed to graze on whatever pasture is available. In Winter hay to feed the animals must be brought in.

How about firewood? You can't just chop a tree down and burn it. The wood has to dry out a bit before it is good for firewood. In winter with frozen lakes and rivers snow is likely your only source of water and that needs to be melted. Your going to need lots of firewood and it isn't going to come strictly from the trees around your camp.

Mountain passes can be impossible in Winter. 6 feet of snow is incredibly difficult to move through without proper gear. Moving heavy equipment is even more difficult. Avalanches are also a hazard and telling your men to be quite isn't likely to save you because your enemies scouts just might know how to yell. Even if your army makes it through just fine who can guarantee that the supplies to your army will make it through.

Campaign season is not just a thing of the past. George Washington crossing the Delaware was a huge surprise because the attack was done during a time when moving troops is incredibly difficult and even dangerous. In WW2 major offensives were planned around the weather. Why did Hitler invade Russia in June? Because in Spring Russian roads are impossible to drive on due to mud. Russian Winters are cold and food is scarce. Fighting in Southeast Asia? Plan your strategy around the Monsoon season.

The climate did vary and we have records of drought, heat waves, cold periods etc. The pollen record in soil gives us a pretty good idea of climate for any time. But the general trend of wet mild springs warm dry summers wet mild fall and cold wet winter has defined the climate of Europe for thousands of years. In general though Campaign Season is much less of a tradition than a natural physical limitation. There are tales of impressive victories when people overcome this limit but there are far more tales of tragic defeats when this limit was not overcome.