It would make sense for there to be a separate modifier or an exception for creatures that are bred to be beasts of burden, which would make sense. A pony is medium and has STR 13, but a real-life pony can carry more than a lion can, even though a lion is STR 21 and Large. They use their strength in different ways.
Actually, STR 13 really doesn't make sense for a pony. A "realistic" stat block would put that figure much higher.
A pony is just a small horse. But small is a relative term; they tend to be short-coupled and have shorter legs, but are not half the length and height of a typical horse, as is implied in the size rules for the game. Officially a horse of 14.2 hands high or less is a pony; if it is 14.3 hands it is a horse. There are many breeds which taxonomists disagree whether they are horses or ponies. If they are to be considered medium creatures then they must be understood to be at the upper limit of possible size for a medium creature. The problem is solved if we apply the modifier for a large creature instead.
I've been doing some research and have found that ponies are typically considered to be sturdier and heartier than horses, which explains why they were kept despite their small size. They are also stronger proportionally (i.e. relative to their body weight) than horses, and a pony can be expected to be able to pull a load equal to about 4.5 times its weight.
The ponies of the Pony Express would carry a load of 165 lbs. (75 kg). Not all the mounts used by the Pony Express were ponies, though many were, and they were more common on the mountainous portions of the route. And they had to be able to run.
The United States Pony Clubs inc. is an organization that promotes sports involving ponies. The mounted games require the rider to weigh-in before a game, and these are the limits:
12.2 hands high and under: 117 lbs
13.2 hands high and under: 150 lbs
14.2 hands high and under: 190 lbs
So clearly a limit of 150 lbs is fairly reasonable. Some ponies ought in fact be able to carry more, but these are mentioned in the description as "variant" ponies (like heavy horses).