Pigs are dangerous animals. My dad had a friend who was a hog farmer, and he never let us kids get near the hogs when we visited. Just Google "pig attack statistics" to see a long list of incidents where pigs killed people. These lists usually include other livestock as well, but pigs are always specifically mentioned.
Pigs will knock you over, then trample you, then decide you are on today's menu:
Pig Bites Man - How often do livestock deliberately kill farmers?
You don't need a massive wild boar like Willk mentions, since a large "domestic" boar, or even sow, can be very large. Wikipedia states that even a domestic pig can get to be 770 lbs. Most pigs sold for slaughter are sold at around 200-220 lbs due to fat content, not because they reached a "final" or adult size. (Market sales are more about Return On Investment, and feeding pigs over a certain size doesn't necessarily increase their size at the same rate as feeding a smaller pig.)
BTW, when you are near a large pig that isn't happy about something, the last thing you think is how pink and cuddly this animal is, who is squealing, thrashing, and generally being violent. Just ask any farmer or veterinarian who has had to vaccinate hogs!
Not only was my dad's friend a farmer, but my dad was a farmer, too. We raised sheep and we would sometimes put our rams on a leash to get to better grazing. (We didn't have a dog trained for sheep herding, so a leash was it.) (The rams were in individual small pens that were usually overgrazed.)
As a pre-teen, I would sometimes jump on the back of the ram I had and "go for a ride". The ram was smaller than some pigs I've seen at fairs and other farms, and this ram had no problems taking off at a run with me on his back.
Trained correctly, a pig could definitely be an alternate to a horse. And yes, pigs are pretty smart. Just don't fall asleep too near the pen, or you might wake up to being chewed on!