We know who the serpent really is. 2 Nephi 2:18 reads
And because he had fallen from heaven, and had become miserable forever, he sought also the misery of all mankind. Wherefore, he said unto Eve, yea, even that old serpent, who is the devil...His misery is related to his nakedness or inability to one day be "clothed" in glory or "covered" by the atonement. The "naked" or furless serpent works well as a symbol for this. But there is something else about the serpent too: God cursed it to crawl upon his belly and eat dust all the days of his life (Genesis 3:14). In other words, he would never be able to "arise from the dust" (2 Nephi 1:14). Consequently, if we don't arise from the dust either as Lehi exhorted his sons, we will stay in the realm of the Devil, the "dust-eater" and might be consumed by him. This is what happens if we don't put off the natural man (Mosiah 3:19) or the flesh, which was formed from the dust. On the other hand, if we put off the natural man and arise from the dust, we will just like Christ have the power to "bruise his head" while he can only "bruise our heel".
I think there is some interesting symbolism to contemplate here.