"penetrate the dense darkness that surrounds them. He will reveal to them the truth as it is in Jesus, and many will yet take their position with His people. GC 565.3"
"And ye shall know the truth, and the truth shall make you free."
EGW speaks of revealing the truth as it is in Jesus, and John 8:32 states that knowing the truth will make you free. The connection is that the truth (specifically, the truth about Jesus) leads to liberation.
"But Romanism as a system is no more in harmony with the gospel of Christ now than at any former period in her history. The Protestant churches are in great darkness, or they would discern the signs of the times. The Roman Church is far-reaching in her plans and modes of operation. She is employing every device to extend her influence and increase her power in preparation for a fierce and determined conflict to regain control of the world, to re-establish persecution, and to undo all that Protestantism has done. Catholicism is gaining ground upon every side. See the increasing number of her churches and chapels in Protestant countries. Look at the popularity of her colleges and seminaries in America, so widely patronized by Protestants. Look at the growth of ritualism in England and the frequent defections to the ranks of the Catholics. These things should awaken the anxiety of all who prize the pure principles of the gospel. GC 565.4"
"And in the morning, It will be foul weather to day: for the sky is red and lowring. O ye hypocrites, ye can discern the face of the sky; but can ye not discern the signs of the times?"
Both passages emphasize the importance of discerning the signs of the times. Matthew 16:3 criticizes the inability to recognize these signs, while EGW laments the Protestant churches' failure to discern the signs related to the resurgence of Romanism.