The 'Witches' Rune', a chant originating from Gardnerian Wicca, refers to the Wiccan God with the very apt line 'Hornèd hunter of the night'.
The most often cited influences for the Wiccan God are Cernunnos and Pan, two of the best known European 'horned god' figures.
I take Cernunnos primarily as a visual influence, since the reality is that practically nothing is known about him or his cult. While several images of horned deities have been discovered in Celtic regions, the name itself is based on just one inscription. There are no references to him in classical literature. Based on the images, we can surmise that the Celtic horned god had a close connection with animals, but that's pretty much it.
Pan, on the other hand, is rather better known from classical sources. As a god of nature and fertility, he is of course an iconic pagan figure. (One of the most interesting myths of Pan from a Wiccan viewpoint has to be the seduction of the moon goddess Selene, whom he tricked by wrapping himself in a sheepskin. Even though Pan's appearance is of course goat-like, the phrase 'wolf in sheep's clothing' springs to mind - and indeed, when I think about the relationship of the God and the Goddess, I can't help but think of the classic motif of the wolf howling at the moon...)
I see the Horned God as a primal figure, a personification of instinct, desire, and vigour (virility, even). He could perhaps be seen as a representative of the Id. More externally he personifies these same forces in nature, i.e. the fundamental elements of life itself, growth and fertility. Cernunnos, Pan, as well as 'Green Man' figures that are sometimes associated with the God in Wiccan traditions, all have in common the fact that they combine human features with nature, which is probably the most important clue as to his nature that we have.
In the daytime it is easy to picture him walking in woods, particularly in the spring and summer, while at night one might picture him seated near a fire, perhaps performing shamanistic rites.
An aspect of the God emphasised by many Wiccan authors is that of the solar deity, but frankly, I don't really see this. Yes, the sun is a vital part of life on Earth, steeped in symbolism, but, apart from a superficial connection to growth and fertility, it doesn't really fit the feel of the Horned God, who is a much more earthy figure. Since I also see deities as primarily inhabiting our subjective realities, and the sun basically as little more than a gigantic burning ball of gas, I don't really see much point in exploring this aspect much. But this is of course a matter of personal taste.