I am curious as to what condition they awoke in. Does it specify, or is it left to the reader's imagination?
We know practically nothing about the physical state of the Children of Ilúvatar at the time of their awakening. In the published Silmarillion, the awakening of the Elves is described very simply:
It is told that even as Varda ended her labours, and they were long, when first Menelmacar strode up the sky and the blue fire of Helluin flickered in the mists above the borders of the world, in that hour the Children of the Earth awoke, the Firstborn of Ilúvatar. By the starlit mere of Cuiviénen, Water of Awakening, they rose from the sleep of Ilúvatar; and while they dwelt yet silent by Cuiviénen their eyes beheld first of all things the stars of heaven.
The Silmarillion III Quenta Silmarillion Chapter 2: "Of the Coming of the Elves and the Captivity of Melkor"
The awakening of Men is similarly vague:
At the first rising of the Sun the Younger Children of Ilúvatar awoke in the land of Hildórien in the eastward regions of Middle-earth; but the first Sun arose in the West, and the opening eyes of Men were turned towards it, and their feet as they wandered over the Earth for the most part strayed that way.
The Silmarillion III Quenta Silmarillion Chapter 12: "Of Men"
As near as I can tell, none of the drafts in History of Middle-earth offer more detail than this; there's certainly no reference to clothing that I can find.
There is a very early draft (the earliest, from The Book of Lost Tales) that describes Men in slightly more detail, but offers no hints at answering this question:
Now did Nuin descend deeper into the vale, treading softly by reason of some unknown wonder that possessed him, and lo, beneath the trees he saw the warm dusk full of sleeping forms, and some were twined each in the other's arms, and some lay sleeping gently all alone, and Nuin stood and marvelled, scarce breathing.
History of Middle-earth I The Book of Lost Tales, Part One Chapter 10: "Gilfanon's Tale: The Travail of the Noldoli and the Coming of Mankind"