The only transportation some 120K years ago would have been limited to walking and for great distances, long boats.
I suspect women were less likely to travel outside the area of their childhood, unless, the whole tribe was trying to escape some oncoming threat or place of disease.
I don’t think man was even to the point of using horses that early in civilization.
Horses were only tamed for horseback riding about 6,000 years ago. They launched the steppe herder Yamnaya people on a 2,000-year-long conquest of Europe, the Middle East, North India, and Central Asia. Today, most European males trace their patrilineal lineage to the horse-taming Yamnaya.