I am just starting to learn Russian and I noticed that these 2 words are very similar. Are they actually related? Is a square a place to keep your horse? Thanks in advance.
They are not related any more than English "mare" and "square" are.
Лошадь is believed to originate from Turkic languages.
Площадь is a native Russian word, ultimately from a Proto-Indo-European etymon, which is also a distant ancestor of the English word "flake".
There are lots words in Russian. For purely statistical reasons, coincidences like this are dime a dozen.