What period? What place? A soldier for whom? Attacked by whom? Going where?
If this guy is a Gaul ambushed by political enemies of his family in the time of Julius Caesar, near his home, it's a different story than a Legionnaire in North Africa during the Punic War. Starting w/road regs differ.
First, there were different classes of roads. The ones you think of, made all of stone, last for thousands of years, are primary military roads. They existed to marcih the Legions on. In many places, there simply wasn't one, and the local road was improved dirt. Traffic on the big roads was limited, to prevent wear and tear. Cartwheels are the worst, so only occassional light buggies or official wagons got the go. Otherwise, everyone was walking or riding on an animal.
Because of this, outside of cities, except for short hauls, merchandise moved on sumpter beasts, not wagons. So your caravan is a good choice: merchants and guards on horses leading pack mules or pack horses.
Your character might ask permission to tag along. The chief merchant might okay this if he doesn't look dodgy. Thing is, most horses can't carry two riders: they aren't up to the strain. There would have to be a horse free for him
He might volunteer to join the guard in exchange for food & a mount until they get to X.
Lionel Casson, Travel in the Ancient World
Jack Coggins, The Horseman's Bible
US Army, Field Manual #25-7 on sumpter mules & horses
Ann Hyland, Equus