The boots are an element of Estragon, while the hat is an element of Vladimir. Just as the hat is representative of Vladimir's role as a thinker and philosopher, the boots show us that Estragon is the more "earthy" character... more emotional, a more concrete thinker, and less convinced that this unknown man Godot will actually show up. As an earthy character, Estragon is more concerned with the moment than Vladimir is, and thus is easily distracted from his own suffering. Just like with Pozzo and Lucky, these "joined" characters represent opposite characteristics.
The boots, like the hat, are also symbolic of civilization and the human condition. Civilization tells us that boots are a necessary part of life. However, Estragon's boots are too tight and hurt his feet, in the same way that civilization restricts human behavior and can cause pain, such as alientation and loneliness. Estragon's daily struggle with his boots shows how humans are trapped into other such daily struggles. Each day is a challenge and is full of difficulty, even if that difficulty seems relatively minor.
I am not actually answering the question, but the previous response is interesting.
I once saw a production, back in (about) 1980 and the two characters (V and E) spent most of the production trying on hundreds of boots) none of which were a pair. It might sound 'dull' but it actually made for interesting and effective theatre the way it was put together.