The reason for a fighting season is based primarily around logistics and supply. A consequence to the pre-modern technological developments, armies could only really operate effectively during the fighting season, usually from mid/late spring to mid-autumn.

(Now at this point I must confess that my thesis was on pre-modern military supply and logistics so apologies if I ramble on a bit much – I found a question which connects to my topic.)

Let us first take roads. Unmetalled roads (gravel, dirt, etc) are extremely prone to damage and flooding in poor weather, and what is more, when wet, the road surface rapidly becomes impassable for anything other than tracked vehicles. If you were to attempt to send any amount of troops down that road, even an average muddy track would be churned into a gloopy, clinging, morass after the first regiment, and subsequent units would make it even worse. One of the reasons the front of the line of march was seen as a so prestigious throughout history may not solely have been “first in contact with the enemy” but rather “it’s a much easier time of it to march”. Bad enough for men, who are exhausted and tired after marching any distance in such conditions. However, it is arguably even worse for the animals of the army which, pre-modern, meant horses. Deep mud such as what these roads would be by the time the logistical arm of the force used them, can damage horses muscles and tendons, and when a horse falls over, whether in pack or in draught, it can be deadly to the horse. Once of the major factors in keeping your army moving and supplied was the availability of suitable horses and any campaign rapidly wears down those numbers, in poor weather and in poor road conditions it is even worse. Armies, where possible, would instead prefer to base their logistics on rivers rather than roads, and again, if in winter these might be too impassable, and certainly the army marching along or near the roads upon which their logistics ran would suffer the same mud and movement issues as roads themselves. AN example would be Gustavus Adolphus’ initial campaigns during the Thirty Years War – they basically follow a map of the major rivers in Germany.

Tied to this, and for any army whose transport is based on horses, as well as cavalry or dragoons, is the availability of fodder, or fresh grass. Now, while modern science has told us of the importance of fresh grass to a horse’s diet, the sheer fact is that a horse needs to do almost nothing but eat grass for most of a day in order to get enough of its minimum energy requirements solely from that. If you are expecting those horses to be carrying men, pulling loads, towing artillery, etc., for hours and hours then it needs a richer, more energy efficient method of food. Here comes in another element of the fighting season – the horses need oats and other cereals and pulses, in addition to grass or hay, to eat so that they can spend most of the day working, rather than eating. The problem here is that most of the crops suitable for these purposes are also needed for much the same reason – high calorie content – for the troops. This, ideally, needs to be found while on campaign and the important of cavalry for premodern armies comes into its own here. Mounted men travelling perhaps days from the army’s line of march, scoured the lands around to gather in supplied for the marching army. These foragers supplemented the food the men could source at each of their stops. Most cereal crops – rye, wheat, oats, etc. were harvested around August, with pulses like peas usually available a little earlier, say June or July. However, cereal crops were most often cut when ripe, stored on the sheaf and then only thrashed to produce what grain was needed at that time, for almost 9 months they could be stored on their cut stalks in bundles.

Now, onto those troops. Your force is marching all day, and when it comes to its assigned billet, it takes the food from among the civilians there. This was an imperfect system, but utterly essential in the days before canned goods. Men could carry very limited amounts of food with them, in addition to their heavy equipment and arms. The most portable foods in military terms, well into the nineteenth century were bread (or biscuit, a type of hard loaf baked multiple times) and cheese. Other food types could travel well over long distances, but these tended to be extensively preserved such as salted meat. These ‘preserved’ foods also needed extensive preparation time to be edible, heavily salted meat might need to be boiled several times with the water replaced at each boiling in order to be edible. For men finishing a long march, with a few hours sleep before marching again, this was not really an option. In barracks over the winter, or for a forts garrison – yes, but those had different experiences all round and are not really important to the reasons for a ‘fighting season’.

Late winter and very early spring was when domesticated animals often birthed and weaned their young, so by late spring there were also plenty of fresh meat walking around on four legs for the soldiers to also make use off, but if taken on the march (a tricky and difficult task) they also needed to be fed – perhaps another reason why you had to wait until there was enough grass to keep your food supply alive until you ate it.

I’ll cut it off here as otherwise I might bore you with more details (oh yes, there is more, much more) but the answer to your question is basically food, roads, and reliable supply. That is the main reason for the ‘fighting seasons’ of the past. With the advent of canning, improved logistical support through railroads and eventually the provision of transport along largely metaled roads, or at least by internal combustion engine, the ability to fight, or at least to campaign in large numbers all year round was complete.

Further reading:
van Creveld, M., Supplying War: Logistics from Wallenstein to Patton, 2nd edition (Cambridge University Press, 2004)

Hess, E., Civil War Logistics, A study of Military Transportation (Louisiana State University Press, 2017)

Lynn, J. (ed.), Feeding Mars: Logistics in Western Warfare from the Middles Ages to the Present (Westview Press, 1993)

Parker, G., The Army of Flanders and the Spanish Road, 1567-1659: The Logistics of Spanish Victory and Defeat in the Low Countries’ Wars, 2nd edition (Cambridge University Press, 2004)