Gollum was probably not initially a hobbit, and is never explicitly described as such in any edition of The Hobbit. Tolkien decided that Gollum was a hobbit at some point early on during the writing of The Lord of the Rings.
In The Hobbit (the final edition, revised to better fit the unplanned sequel The Lord of the Rings), Gollum is introduced thus:
Deep down here by the dark water lived old Gollum, a small slimy creature. I don't know where he came from, nor who or what he was. He was Gollum — as dark as darkness, except for two big round pale eyes in his thin face.
The revisions of the Gollum chapter change his motivations, but not his physical appearance nor his backstory. We are told that
Riddles were all [Gollum] could think of. Asking them, and sometimes guessing them, had been the only game he had ever played with other funny creatures sitting in their holes in the long, long ago, before the goblins came, and he was cut off from his friends far under under the mountains.
Gollum brought up memories of ages and ages and ages before, when he lived with his grandmother in a hole in a bank by a river (…)
Gollum remembered thieving from nests long ago, and sitting under the river bank teaching his grandmother, teaching his grandmother to suck—"Eggses!" he hissed.
None of this is conclusive one way or another. There's a theory that these details foreshadow Gollum's being a hobbit: his living in a hole, his familiarity with the same kind of riddles as Bilbo. Yet these characteristics could easily apply to all manner of fantastic creatures. In particular, the original Gollum was not corrupted by the Ring — since the original ring was just a bauble that made the wearer invisible.
Moving to out-of-story evidence, Christopher Tolkien's History of The Lord of the Rings discusses the early drafts of the Gandalf's account of the origins of the Ring and of Gollum (what would become parts of chapter 1 and chapter 2 of book 1). (Part 1: The Return of the Shadow, III: Of Gollum and the Ring.) In the earliest extant draft, Tolkien wrote: (Gandalf (or maybe Gildor, an Elf whose expository role would eventually become Gandalf's) speaks to Bingo, Bilbo's son, whose role would eventually become Frodo's.)
Do you remember Bilbo's storyof Gollum? We don't know where Gollum comes in — certainly not elf, nor goblin; he is probably not dwarf; we rather believe he really belongs to an ancient sort of hobbit.
A crossed-out sentence reads “Gollum I think some sort of distant kinsman of the goblin sort”.
A later draft is a lot closer to Gandalf's tale in the final version, though less furnished with details:
‘There aws long ago living by the bank of the stream a wise, cleverhanded and quietfooted family. I guess they were of hobbit-kind, or akin to the fathers of the fathers of the hobbits. The most inquisitive and curious-minded of that family was called Dígol.’
‘Gollum!’ said Bingo. ‘Do you mean that Gollum that Bilbo met? Is that his history? How very horrible and sad. I hate to think that he was connected with hobbits, however distantly.’
‘But that surely was plain from Bilbo's own account,’ said Gandalf. ‘It is the only thing that explains the events — or partly explains them. There was a lot in the background of both their minds and memories that was very similar — they understood one another really (if you think of it) better than hobbits ever understood dwarves, elves, or goblins.’
The final version isn't as assertive as to the premonitory quality of Gollum's similarities with Bilbo:
‘Gollum!’ cried Frodo. ‘Gollum? Do you mean that this is the very Gollum-creature that Bilbo met? How loathsome!’
‘I think it is a sad story,’ said the wizard, ‘and it might have happened to others, even to some hobbits that I have known.’
‘I can't believe that Gollum was connected with hobbits, however distantly,’ said Frodo with some heat. ‘What an abominable notion!’
‘It is true all the same,’ replied Gandalf. ‘About their origins, at any rate, I know more than hobbits do themselves. And even Bilbo's story suggests the kinship. There was a great deal in the background of their minds and memories that was very similar. They understood one another remarkably well, very much better than a hobbit would understand, say, a Dwarf, or an Orc, or even an Elf. Think of the riddles they both knew, for one thing.’
‘Yes,’ said Frodo. ‘Though other folks besides hobbits ask riddles, and of much the same sort. And hobbits don't cheat. Gollum meant to cheat all the time. (…)’
A few of Tolkien's collected letters touch on Gollum. Worth citing are:
Letter 25, to the editor of the ‘Observer’ (January 1938):
And what about the Riddles? There is work to be done here on the sources and analogues. I should not be at all surprised to learn that both the hobbit and Gollum will find their claim to have invented any of them disallowed.
Letter 70, to Christopher Tolkien (May 1944)
Gollum continues to develop into a most intriguing character.
Letter 109, to Stanley Unwin (July 1947)
Nor is it Bilbo's actions, I think, that need explanation. The weakness is Gollum, and his action in offering the ring as a present. However, Gollum later becomes a prime character, and I do not rely on Gandalf to make his psychology intelligible. I hope it will come off, and Gandalf finally be revealed as perceptive rather than 'hard put to it'. Still I must bear this in mind, when I revise chapter II for press : I intend, in any case, to shorten it.
Also worth mentioning is letter 214, to A. C. Nunn. Mr Nunn was a reader who noticed that in The Lord of the Rings, Tolkien states that Hobbits give presents to other people on their own birthdays; yet Gollum received the Ring on his birthday and counted it as a birthday present. In his answer, Tolkien expounds on the birthday customs of the various branches of hobbits. The relevant fact here is that Sméagol was a Stoor. Stoors are one of the three races of Halflings (as Men call them), the other two being the Harfoots (to which the Shire-folk belong) and the Fallohides. The term “hobbit” originally was the Fallohides' and Stoors' name for Harfoots, and later came to encompass all Halflings (The Lord of the Rings, appendix F).
My reading of the evidence is that Gollum was originally meant to be just another mysterious fantasy creature. Early on in the writing of The Lord of the Rings, Tolkien decided that Gollum was in fact a hobbit, or close thereto. In any case, Gollum absolutely is a hobbit in The Lord of the Rings; in the final version of The Hobbit, this is left unsaid, to be revealed in the sequel.