The point was that the artillery pieces themselves were drawn by teems of draft animals. Outside of Europe with a decent road network, long cross country moves might require that they be moved by sledge rather than by their wheels but on good roads they were of little encumbrance. Foot artillery and most wagons in the trains would have been pulled by oxen which were good at hauling loads but not noted for their speed.

Up to this point in TW games supply has not been a factor of movement. In fact the whole idea of moving with artillery prior to gunpowder is a bit silly. Most of the machines were built on the site rather than transported and artillerists had a whole different skill set. Some may have been disassembled and moved.

You can march a column of horses at about 60 miles a day (100 km) and Infantry about 20 miles (roughly 34 km) sustainable. Living off the land slows this progress considerably. Drinking water was not an option in most places and the troops had to brew their own beer as well as bake their bread. Foraging off the land is one thing when it mean robbing peasants and another when it is finding food in a wilderness, while being watched by an indigenous force, likely hostile…

Diseases killed hundreds and sometimes thousands in campaigns, usually about twice what the enemy could manage.

There is good reason why we can accomplish in a game what no one did in these times. I don’t think we would like it so well if it were truly realistic, even in the age of reason.