When God made Adam and Eve, He made them in His image. Throughout the Bible, that "image" is represented as being His perfect character, and the skin or its covering is a symbol of character.
For example, God says:
Can the Ethiopian change his skin, or the leopard his spots? then may
ye also do good, that are accustomed to do evil. (Jeremiah 13:23, KJV)
This likens one's character to his skin. And in Revelation we also are given instructions to "wash our robes."
And I said unto him, Sir, thou knowest. And he said to me, These are
they which came out of great tribulation, and have washed their robes,
and made them white in the blood of the Lamb. (Revelation 7:14, KJV)
The sacrificial animals brought to the temple were not to have any blemish in their skin because they were to represent Jesus whose character was perfect and sinless just as the characters of Adam and Eve were sinless and perfect when they were created in God's image.
And how is God clothed?
Who coverest [thyself] with light as with a garment: who stretchest
out the heavens like a curtain: (Psalm 104:2, KJV)
[Note that the word "thyself" is supplied in the KJV and, if removed, could also apply to God's creation.]
God had created Adam and Eve in His likeness. As God was covered in a robe of light, so were they. But they lost this when they sinned. That is when they noticed that they were naked. They also felt a sense of chilliness which they hadn't noticed before.
And they heard the voice of the LORD God walking in the garden in the
cool of the day: and Adam and his wife hid themselves from the
presence of the LORD God amongst the trees of the garden. (Genesis
How well would fig leaves, or any green leaves for that matter, protect against the chill of the evening? Not very well, to be sure. God knew they needed something more.
Unto Adam also and to his wife did the LORD God make coats of skins,
and clothed them. (Genesis 3:21, KJV)
More than this, the leaves, as compared to the garments of skins, could not represent the remedy for the sin which had brought them into this need. The leaves, being purely of plant origin and without blood, could no more represent the sacrifice and cost to God that their sin had caused than could Cain's offering atone for his sin.
And almost all things are by the law purged with blood; and without
shedding of blood is no remission. (Hebrews 9:22, KJV)
The coats of skins which God made for the guilty pair cost the life of some animal(s). It was a lesson to both of them in how much their sin would cost. This lesson would have been entirely absent had the fig-leaf covering been sufficient to cover their shame.
So, both for physical warmth and protection, and for the spiritual lessons embodied in the representations made of them, there was a wide difference between the fig-leaf coverings Adam and Eve had made for themselves and the coverings of skin which God made for them.