A horse can only run about 30 miles an hour. So, if the horse pulls a carriage it can only go as fast as the horse can go. The speed would be about 30 miles an hour.
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It would go as fast as the horse pulling it, which is about 30-35 miles an hour at full speed.
The speed would be that of the horse that pulls it, at top speed about 30-35 miles per hour.
A wagon is typically pulled at a walk or trot so the speed would range between 4 mph and up to 10 mph.