Isaiah is dealing in symbolic vision, not television. Just as the robe of God symbolically but not literally fills the temple, so the beings Isaiah sees are symbolic, not literal. He sees them, but it is the meaning of their image that is much more important that the image itself.
Symbolic analysis: The word “seraphim” is a plural, easily understood when Isaiah notes “each one…”. The word comes from a word with the meaning of “burning.” It is an important meaning that is lost in our translation, as the burning aspect would certainly have illustrated their glory, and this brightness or burning would have marked them as celestial beings.
The wings are clearly related to flight, because “with twain did he fly.” However, once again, it is the wing as a symbol of movement or mobility that is more important that the wing itself. This is specifically true with the non-flight-related functions of the other two sets of wings.
Gileadi gives a reading for the symbolic covering of the face and feet:
Seraphs stood by him overhead, each having six wings - with two they could veil their presence, with two conceal their location, with two fly about. (Gileadi, p. 106.)
While “presence” and one’s “face” do appear to have an association in the scriptures, and “feet” and “location” have a logic, they do not appear to fit this context as well as the original. One must remember that Isaiah is seeing the seraphim, and therefore their location is certainly not concealed, nor is their presence veiled. Isaiah clearly sees them in the presence of God, and it is that presence that provides the best context for understanding the wings that cover face and feet.
The experience of Moses before the Lord, and then before Israel gives us the best context for this idea:
Ex. 34:33
33 And till Moses had done speaking with them, he put a vail on his face.
Ex. 34:34
34 But when Moses went in before the LORD to speak with him, he took the vail off, until he came out. And he came out, and spake unto the children of Israel that which he was commanded.
Ex. 34:35
35 And the children of Israel saw the face of Moses, that the skin of Moses’ face shone: and Moses put the vail upon his face again, until he went in to speak with him.
In Exodus 34:35 note the shining of Moses’ face. The “burning ones” or seraphim and the shining face of Moses have their origins in the same concept of the glory of God. Moses receives this, and the people must be protected from it. Thus in Moses’ case, the veil is a protection - a barrier between glory and those who might be harmed by the overwhelming glory of the Lord.
Now the question is who is being protected in Isaiah’s case. The symbol is the same, there is a protective covering between someone and glory. In this case, however, it is not Isaiah who is being protected from the seraphim’s glory. Isaiah is already beholding the glory of God, which necessarily is greater than that of the seraphim.
The rest of the question lies in the nature of the regions of the body. The head was considered to be a very susceptible part of the body, probably a symbolic extension of the soft spot on the crown of a baby’s head. Thus this part of man is symbolically thin, and power can more easily enter there. For this reasons, blessings and annointings are give on the crown of the head.
This is also the reason for the covering of women’s heads in Paul:
1 Cor. 11:7
7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
In Paul, however, men have become strong enough (through the priesthood?) that they can withstand the symbolic presence of God in a church gathering. In Paul’s theology, women still require such protection on the crowns of their heads.
Thus when the faces of the seraphim are covered, they are covering a vulnerable portion of their body from the glory of God. Whether the feet are significant here of the connection to earthly endeavors (Moses’ has to put off his shoes on holy ground) or whether the protection of the “feet” is the euphemism for genitalia, the concept is the same. While Isaiah is seeing the seraphim, what he is symbolically describing is the overwhelming glory of God.