This question is complicated, so hang on. A medieval army made up mostly of foot soldiers wearing plate armor (although there are cavalry, they're going at the speed of the foot soldiers) with enough supplies to last them the journey carried in horse-drawn carts that go at the same speed as the foot soldiers. The land they walk contains enough water for drinking, cleaning, and other purposes. The soldiers walk for twelve hours every day.
The total length of the journey is roughly 360 miles (579 km). Of that, about 150 miles (241 km) are in grasslands composed of rolling hills while the rest of the journey is in forest. None of the march in the grasslands is on marked roads, while half on the walk in the forest (105 miles or 169 km) is on maintained roads while the rest is not.
The army leaves in the middle of November (I don't use exact dates in my story, but if you need one, say November 15) and the area has a climate similar to that of the states of Virginia and North Carolina.
The army collects more soldiers as they go. They start the journey with 5,000 soldiers and end with 25,000. For the sake of the question, let's say they collect new soldiers at a steady rate. I don't know how this would affect the army's pace.
All of this is really for the background detail of whether they arrive in winter or spring, but still, if the army makes no long stops and keeps a steady pace, how long will it take for the army to get from point A to point B?
I have a hard time figuring this out because of all of the details, but here's a source I found. It doesn't talk about biomes, roads, climates, and gathering more soldiers, but it has some details about pace that might help.