What does the naked man signify?

As with all of Greenaway's movies there's layer upon layer of symbolism and structure going on in TDC. My take on most of his films, though, is grounded in the general idea that Greenaway's attitude towards filmmaking is a painterly one. He favors carefully composed imagery over plot; there's plenty of the latter, but it's usually through the former that the real meaning of his films comes forth.

The Draughtsman is an idealist who believes that he can impose an order on his surroundings both directly through his work (he claims that his drawings reproduce exactly what he sees) and through the contract with Mrs. Herbert (whereby he's allowed regular access to her entirely on his own terms).

But the goal of perfectly representing reality on a piece of paper is fruitless; the Draughtsman's output is static, orderly, and enclosed, while real life is messy and complicated (and ultimately inflicts itself on the Draughtsman as a messy death). The appearance and disappearance of objects like the ladder and washing from day to day frustrate Mr. Neville's goals, and I believe the "living statue" is a similar symbol of the unpredictability of the real world. A classical statue should be a prime example of the Draughtsman's attitude towards reality and art---the statue captures an ideal form, a fixed reproduction of humanity with none of humanity's imperfection and unpredictability---but Greenaway instead plays a joke on the Draughtsman and the viewer by having the "statue" live, breathe, move around, and amuse itself with juvenile bathroom humor.

In the film, Mr Neville and Mrs Talmann debate the value of classical allusions. There is also reference to there being a statue of Bacchus in the garden. Bacchus was a God associated with virility, so if we assume that the living statue is supposed to be Bacchus, we might view it to symbolise the sexual aspects of Mr Neville's personality, which are forever present, consciously or unconsciously, in the plot and in the minds of the characters, much as the statue is forever present in the garden, though rarely acknowledged by characters. The statue seems to 'haunt' the garden, in the same way that Mr Neville's intimacy with the two women haunts the male characters, especially Mr Talmann, upsetting the hierarchical order of the estate and causing chaos, as the statue does. Thereby, the statue is seen pulling faces at the nephew, Augustus, who may not inherit the estate if Mrs T was to conceive a male child by Mr N. Also, when (spoiler alert!) Mr N is murdered due to his relationship with the two women, the statue shows cold disregard for the body; instead, it gorges on his pineapple, before spitting it out. It is as if Mr N's promiscuity, as manifested in the figure of Bacchus, overpowered him, led to his downfall, and stands triumphantly over him at his death. Apparently, the value of the living statue was more explicit in an earlier edit of the film, though in the released version, much is left to the viewer's interpretation, another reason why it is such a refreshing and interesting movie!