To give you the short answer: "naked" in the 19th century could be used to mean "completely without clothing" or "without outer clothing." While The Lord of the Rings was written significantly later, it is clear from context that in that book it means the latter. In The Adventures of Huckleberry Finn, it seems to mean the former.

Let's start with Huck. For low-class boys to be without clothing when swimming (or close to water) was not rare; contemporary descriptions have lots of boys diving, swimming, and carrying on in and near water without wearing a thing. The Adventures of Huckleberry Finn seems to suggest Huck means they are completely unclothed: "we was always naked, day and night, whenever the mosquitoes would let us—the new clothes Buck’s folks made for me was too good to be comfortable, and besides I didn’t go much on clothes, nohow."

Meanwhile, in The Lord of the Rings, I believe you're referring to the scene in which Tom Bombadil rescues the hobbits from the barrow-wight. Let's take a closer look: it describes that the hobbits are missing their "cloak, jacket, and breeches", while they are clad "thin white rags, crowned and belted with pale gold, and jingling with trinkets." Clearly not properly naked. (If you meant a different scene, please let me know!) So what did "naked" mean?

I can give you a little information about what a 19th British century man would have been wearing, and what would have been considered "naked." Let's note just how many layers are involved, and which layers a proper man would never remove if he was being properly proper! We start with the vest and drawers. The vest may have sleeves or not, depending on the need for warmth, and drawers would be done up (with buttons, drawstrings, or cloth bands) at the waist and ankle. From ankle down, socks complete a pretty complete level of clothing from toe to chin. Materials would generally be wool, usually flannel, though later finer machine-knitted wool became available as machines made it cheaper. Other materials included cotton. Later, the "combination" became popular, which is the "flannel underwear" ankle-to-neck, long-sleeve garment that appears in Wild West movies, usually bright red and with the flap at the back comically... well, flapping. These were all considered underwear.

A shirt would then be put on over the vest. For most of the 19th century, shirts would have separate collars and cuffs. Over top of the shirt would come a waistcoat, and over top of THAT came the ubiquitous jacket. A respectable man would not be seen by others without his jacket: the overcoat would be the removable outermost garment. A man might might leave his jacket unfastened, leaving his "shirtfront" exposed, which was okay. A man in his "shirtsleeves" (sans jacket) would be either very informal or engaged in hard labor. As you can imagine, with that much clothing, doing heavy work, especially in the sun, would require that man strip "to his shirtsleeves," even (gasp!) rolling his sleeves up. The middle class (and up) would generally wear starched collars (the stand-up style was more popular, while the turned-down style popular today was how the upper class "dressed down"), while the lower class wore a cloth tied around the neck. If you were a laborer in the countryside, you might wear a smock in place of a jacket. Fishermen might wear a jumper.

As I suggested earlier, "naked" could be used to refer to people wearing only underclothes. The plentiful descriptions of the "naked" poor in London could mean that the men were without hats or jackets, and women with their upper chests visible (rather than wearing handkerchiefs around their necks). While a man might walk around his house in his drawers and shirtsleeves, to do so in front of anyone he wasn't very comfortable with would have been considered very uncouth!

As a fun aside that helps illustrate clothes and propriety, in the BBC Pride and Prejudice series, there is a scene in which Elizabeth Bennett stumbles across Mr. Darcy playing English billiards by himself. It adds to the social awkwardness of the scene that Mr. Darcy, clearly not expecting to be seen, has removed his jacket, and is seen in only his waistcoat (he is "in his shirtsleeves"). Later, when we see him join the others, he has put his jacket back on. I'll leave it up to my readers, then, to think about what is suggested by the famous scene where, after Mr. Darcy takes a dip in a pool, he meets Elizabeth Bennett....