The Basic Idea: Hodor wargs into Lyanna's horse and gets stuck there, and that's why he is the way he is.
The Problem: According to warging mythology, the term "warg" applies only to a person who can transfer consciousness into a wolf or dog. The correct term is "skinchanger," but it seems highly unlikely Hodor is even that. Skinchangers are very rare — one man in a thousand is born a skinchanger. What's more, there has been no evidence to suggest Hodor is at all magically inclined. Even something as traumatic as the horse's death might damage Hodor mentally but wouldn't necessarily prevent him from ever skinchanging again. If you want a legit theory about Hodor, try this one.