Scriptures Used To Support Nudism
In addition to the Eden text, other passages of Scripture are used to support nudism. Here are a few:

Bathsheba Bathes In Plain View Of David's Palace
It is quite clear that God strongly disapproved of David's adulterous affair with Bathsheba. Since David's downward spiral all started when he lustfully observed Bathsheba taking a bath, it can legitimately be argued that she simply had no business bathing nude in eyeshot of the king's palace (2 Samuel 11). Was she deliberately trying to seduce David? Scripture doesn't say.

This reminds me of the account found in Genesis 26:8-9. Abimelech king of the Philistines looked down from a window and saw Isaac engaging in some sort of sexual activity with his wife Rebekah. Some translations say they were "sporting" (KJV). Other translations say Isaac was "fondling" Rebekah (NLT). And still other translations say they were "laughing" (ESV). Whatever they were doing, it was in plain site of the king and it was a tip-off that Isaac and Rebekah were not brother and sister, as they claimed, but husband and wife. Whether or not this display of affection involved partial or complete nudity is anyone's guess.

Saul Gives Prophetic Utterances In The Nude (1 Samuel 19:23-24)
Prophets sometimes went nude to make a point, although some contend that they weren't totally nude. One example Is Saul.

So Saul went to Naioth at Ramah. But the Spirit of God came even upon him, and he walked along prophesying until he came to Naioth. He stripped off his robes and also prophesied in Samuel's presence. He lay that way all that day and night. This is why people say, “Is Saul also among the prophets?” (NIV)

Isaiah Walks Around Naked For Three Years (Isaiah 20:1-5)
Another prophet that walked around nude was Isaiah, although again, some claim this did not involve total nudity.

In the year that the supreme commander, sent by Sargon king of Assyria, came to Ashdod and attacked and captured it—at that time the Lord spoke through Isaiah son of Amoz. He said to him, “Take off the sackcloth from your body and the sandals from your feet.” And he did so, going around stripped and barefoot. Then the Lord said, “Just as my servant Isaiah has gone stripped and barefoot for three years, as a sign and portent against Egypt and Cush, so the king of Assyria will lead away stripped and barefoot the Egyptian captives and Cushite exiles, young and old, with buttocks bared—to Egypt's shame. Those who trusted in Cush and boasted in Egypt will be afraid and put to shame (NIV).

Being Naked According To Josephus
However, not everyone agrees that all biblical references to being naked refer to being completely naked. According to the highly-respected Jewish historian Flavius Josephus (37 – sometime after 100 CE), sometimes being naked refers to being without one's usual attire:

(38) Mr. Reland notes here very truly, that the word naked does not always signify entirely naked, but sometimes without men's usual armor, without their usual robes or upper garments; as when Virgil bids the husbandman plough naked, and sow naked; when Josephus says (Antiq. B. IV. ch. 3. sect. 2) that God had given the Jews the security of armor when they were naked; and when he here says that Ahab fell on the Syrians when they were naked and drunk; when (Antiq. B. XI. ch. 5. sect. 8) he says that Nehemiah commanded those Jews that were building the walls of Jerusalem to take care to have their armor on upon occasion, that the enemy might not fall upon them naked.I may add, that the case seems to be the same in the Scripture, when it says that Saul lay down naked among the prophets, 1 Samuel 19:24; when it says that Isaiah walked naked and barefoot, Isaiah 20:2, 3; and when it says that Peter, before he girt his fisher's coat to him, was naked, John 21:7.What is said of David also gives light to this, who was reproached by Michal for "dancing before the ark, and uncovering himself in the eyes of his handmaids, as one of the vain fellows shamelessly uncovereth himself," 2 Samuel 6:14, 20; yet it is there expressly said (ver. 14) that "David was girded with a linen ephod," i.e. he had laid aside his robes of state, and put on the sacerdotal, Levitical, or sacred garments, proper for such a solemnity (Antiquities of the Jews - Book VIII).

Being Naked According To Carl Friedrich Keil and Franz Delitzsch
Carl Friedrich Keil and Franz Delitzsch also do not believe that the prophets went totally naked:

With the great importance attached to the clothing in the East, where the feelings upon this point are peculiarly sensitive and modest, a person was looked upon as stripped and naked if he had only taken off his upper garment. What Isaiah was directed to do, therefore, was simply opposed to common custom, and not to moral decency. He was to lay aside the dress of a mourner and preacher of repentance, and to have nothing on but his tunic (cetoneth); and in this, as well as barefooted, he was to show himself in public. This was the costume of a man who had been robbed and disgraced, or else of a beggar or prisoner of war [Commentary on the Old Testament, 7:242 (Peabody, MA: Hendrickson, 2002).]

Being Naked According To Ian B. Johnson
On the other hand, there are also those who strongly disagree that Isaiah and other prophets wore some clothing. For example, when, God told His prophet Isaiah to go about naked and barefoot for three years, it was as a sign of what the Assyrians were going to do to Egypt and Ethiopia. According to Ian B. Johnson:

Moreover, as ancient armies really did publicly parade columns of their captives literally totally naked both to break their wills (through shame to the point of hopelessness) and as a demonstration of the complete control they had over them, it is not to be imagined that either Isaiah or the Egyptian and Ethiopian captives his demonstration symbolized actually were wearing some clothes. They were [totally] naked.