Christ was following the Jewish custom for a royal entry. The animal on which He rode was that ridden by the kings of Israel, and prophecy had foretold that thus the Messiah should come to His kingdom. No sooner was He seated upon the colt than a loud shout of triumph rent the air. The multitude hailed Him as Messiah, their King. Jesus now accepted the homage which He had never before permitted, and the disciples received this as proof that their glad hopes were to be realized by seeing Him established on the throne. The multitude were convinced that the hour of their emancipation was at hand. In imagination they saw the Roman armies driven from Jerusalem, and Israel once more an independent nation. All were happy and excited; the people vied with one another in paying Him homage. They could not display outward pomp and splendor, but they gave Him the worship of happy hearts. They were unable to present Him with costly gifts, but they spread their outer garments as a carpet in His path…
"Rejoice greatly, O daughter of Zion; shout, O daughter of Jerusalem: behold, thy King cometh unto thee: he is just, and having salvation; lowly, and riding upon an ass, and upon a colt the foal of an ass."
EGW directly references Zechariah 9:9 regarding the Messiah riding on a colt, fulfilling prophecy. This is a clear and explicit allusion.
"As they proceeded, the multitude was continually increased by those who had heard of the coming of Jesus and hastened to join the procession. Spectators were constantly mingling with the throng, and asking, Who is this? What does all this commotion signify? They had all heard of Jesus, and expected Him to go to Jerusalem; but they knew that He had heretofore discouraged all effort to place Him on the throne, and they were greatly astonished to learn that this was He. They wondered what could have wrought this change in Him who had declared that His kingdom was not of this world. DA 570.2"
"And the multitudes that went before, and that followed, cried, saying, Hosanna to the Son of David: Blessed is he that cometh in the name of the Lord; Hosanna in the highest."
Both passages describe the multitude accompanying Jesus into Jerusalem and their expressions of praise and wonder. EGW expands on the questions the spectators were asking, providing more detail to the scene described in Matthew.