To enter the actual Merchant's Square, you have to go around the Palace of Reason. You can see the names of the Milanese who died during the two World Wars on the bronze plaques of the robust medieval pillars.
Here you can get an idea of what the original square was like, completely enclosed between buildings and only accessible from the archways. The well surrounded by slabs that you see at the center is more than five hundred years old. If you're an avid reader, you can go browse the stalls of used books under the nearby arcades.
On the other side of the square in front of the Palace of Reason, you can see a row of palaces of various ages that form a fascinating whole. A bank is presently at the center, where there was once a luxurious 14th-century home called Loggia degli Osii: its portico and loggia in black and white marble can still be admired.
If instead you'd like to combine art and food, enjoy lunch in the restaurant which was once the fifteenth century Casa Panigarola while admiring the refined terracotta decorations of its arches.
Now go back to the Palace of Reason at the center of the square. In a central recess on the first floor you can see a horse statue depicting Oldrado da Trésseno, who was the thirteenth-century politician responsible for Merchant's Square and the construction of the Palace of Reason.
FUN FACT: you can see a small Roman bas-relief under an arcade that depicts the so-called "Woolly Sow". Long before the snake of the Sforzas, the symbol of Milan was precisely this cute little pig. According to legend, the founder of the city, who belonged to the ancient Celtic population, saw the animal in a dream in exactly this point.