Symbolism, Imagery, Allegory
From Actaeon to Bambi, deer tend to be symbols of naivety and vulnerability. If you want to take someone down a peg, you could probably do a lot worse than transforming him into a sweet deer.
So by transforming Actaeon into a stag, Artemis captures the spirit of his guilelessness. Especially if he came upon her by chance. Of course, as a scared stag, you're also at the mercy of the world around you. This is a "tables have turned" situation for Actaeon, since just hours before, he was the hunter. He was so in control that he even led a whole group of macho men through the woods as they killed animals; most of which were—you guessed it—deer.
To add insult to injury, the deer was one of Artemis's symbols. So although Actaeon invaded her personal space by barging into the grove, one could argue that she takes ownership of the situation by transforming his body into her personal symbol.
The helpless deer motif has remained tried and true in literature, and was one of Shakespeare's favorite symbols. Jacques's anguish over a wounded deer in As You Like It is particularly memorable, as his weepiness provokes the other characters to make fun of him. And of course, there is the ultimate Poor Deer: Bambi's mom. Oh, Bambi's mom. Why did we even bring that up?