On the Road

When you have to cross such vast distance, you need speed, agility, and endurance.
When it is paramount to keep going, you need something that will carry you.
Legs or wheels.
Both need maintenance - the wheels can be replaced (with a bit of time and material, which you might not have), the legs need to be protected.
Which is why, every evening, while the campfires are burning, there are the sounds of hammers on metal, and neighing, as the new horseshoes are shaped and affixed; and the softer sounds of mallets and needles on leather, shaping, reshaping and darning shoes.