No.
Daniel 8 says "
out of one of them came forth a little horn".
In other words, the little horn replaced one of the original four horns.
It was not another horn in addition to the original horns as was the case in
Daniel 7.
It doesn't say the little horn replaces one of the original four horns that grew to the four winds. What it is emphasizing is that the four break up kingdoms were north, south, east, west.
From the geographic location of one of the breakup kingdoms - has to be the one of the west, in order to go south and east to head toward Israel.... the little horn waxes strong that direction.
Keep in mind at the time Daniel received the prophecy, everything was future. Now at our time in history
part of the overall prophecy is historic.
Conversely, the part about the little horn the vision of him transgressing the covenant it says in the text, Daniel 8:17 below, is time of the end, end times.
The little horn did not replace one of the horns. The four horns representing the breakup kingdoms - happened over 2200 years ago after Alexander. And were subsequently followed by the Roman Empire.
Which in Daniel 7, the Roman Empire, the fourth kingdom has an end times version of it. Which the little horn, end times, first appears among the 10 kings of that fourth kingdom.
Greece, the territory, geographically in our day and time, formerly one of the four breakup kingdoms is the eastern most frontier of the EU in the end times. The EU has a strong army, not the nation of Greece, one of the member nations.
Remember the part about the little horn is end times in the text - while the part about the four breakup kingdoms we know by 20/20 hindsight is historic. With 2000 years of history between us and them. So none of THOSE horns are still around - to be replaced by the little horn.
The intent of Daniel 8:9 is to show where "geographically" the little horn will initially come from with his strong army to the south and east.
13 Then I heard one saint speaking, and another saint said unto that certain
saint which spake, How long
shall be the vision concerning the daily sacrifice, and the transgression of desolation, to give both the sanctuary and the host to be trodden under foot?
14 And he said unto me, Unto two thousand and three hundred days; then shall the sanctuary be cleansed.
15 And it came to pass, when I,
even I Daniel, had seen the vision, and sought for the meaning, then, behold, there stood before me as the appearance of a man.
16 And I heard a man's voice between
the banks of Ulai, which called, and said, Gabriel, make this
man to understand the vision.
17 So he came near where I stood: and when he came, I was afraid, and fell upon my face: but he said unto me, Understand, O son of man:
for at the time of the end shall be the vision.
So the vision of the transgression of desolation by the little horn is end times, 2000 years after the four breakup kingdoms were followed by the Roman Empire.
The transgression of desolation will be when the person goes into the temple sits, claims to be God, in 2thessalonians2:3-4
23 And in the latter time of their [the transgressors kingdom, not the four break up kingdoms] kingdom [the EU in its final form, which it will evolve into], when the transgressors are come to the full [the ten kings of Daniel 7 are in place], a king [the little horn who comes up amongst them] of fierce countenance, and understanding dark sentences, shall stand up.
"stand up" is an idiom for gets ready to fight, go to war. (it's something animals do, stand on their hind legs, right before they charge into each other) Which that war will be the Gog/Magog invasion appearing imminent. And his staging his EU army in Greece as a deterrent, will be seen by the Jews in the aftermath of Gog's destruction, that he is their long awaited messiah - because one of the main things the Jews expect of their messiah, in their beliefs, is that he fights the battles of God in defending Israel.
The 7 years in Ezekiel 39, following the destruction of Gog's army, is the exact same 7 years of Daniel 9:27, which the prince who shall come [from the EU] as perceived messiah confirms the Mt. Sinai covenant for 7 years - a big speech from the temple mount about the land of Israel belonging to the children of Israel forever. And will be anointed the King of Israel, by the false prophet, making him the Antichrist, the rider on the white horse in Revelation 7, who receives a crown, at the start of the 7 years.
Riding a white horse, because he will be perceived to be the messiah, for a while by the Jews - compared to Jesus, the true messiah, and rightful King of Israel, riding a white horse in Revelation 19, King of Kings, Lord of Lords.
That's how it all fits together.