JOEL - Here is what President Woodruff said in the prayer:

"Heavenly Father, when Thy people shall not have the opportunity of entering this holy house to offer their supplications unto Thee, and they are oppressed and in trouble, surrounded by difficulties or assailed by temptation and shall turn their faces towards this Thy holy house and ask Thee for deliverance, for help, for Thy power to be extended in their behalf, we beseech Thee, to look down from Thy holy habitation in mercy and tender compassion upon them, and listen to their cries. "

The Bible speaks of King Solomon facing the Temple during prayer. And Daniel, who according to Scripture prayed three times daily, looked out the windows of his chamber which faced Jerusalem. In our day it is still a Jewish custom to pray facing the Temple Mount in Jerusalem where a temple used to be and some day will again be. But I think President Woodruff is only figuratively refering to this custom when he talks about the people turning their faces towards the temple. It is the House of the Lord and therefore a place that God might be. So in a sense he is talking about them turning their faces towards God in prayer.
He also said in the prayer:

"Or when the children of Thy people, in years to come, shall be separated, through any cause, from this place, and their hearts shall turn in remembrance of Thy promises to this holy Temple, and they shall cry unto Thee from the depths of their affliction and sorrow "

Here he says they will turn their hearts to the temple as they cry to Him. Whether it be hearts or faces, I think the point is that if they think of the temple as they pray and the covenants they made therein, it will serve as an inspiration and remind them of God and what He can do for them in their time of need.
I have heard of some past LDS church members literally facing the temple to pray; perhaps just following the old Jewish custom. But other than that I don't know of any specific instructions given by a prophet of the church that we should pray facing the temple.