Google Books is your friend. It will often give a fuller context to the abbreviated quotes in the OED:
1860 ‘G. & P. WHARTON’ Wits & Beaux of Society I. 127 In ‘birthday attire’. [The quote marks suggest a non-literal, idiomatic meaning, so probably yes.]
“Yet he does not seem to have repented of this transaction, for soon after he was engaged with Sedley and Ogle in a series of most indecent acts at the Cock Tavern in Bow-street, where Sedley, in ‘birthday attire,’ made a blasphemous oration from the balcony of the house.” [A clear reference to nudity.]
1734 SWIFT Strephon & Chloe in Poems (1958) II. 591 To see some radiant nymph appear In all her glitt’ring birthday gear. [Having read the whole poem, which is about a young man somewhat disillusioned to find that his new bride pees, poops and farts like any mortal, I would say this one counts, at least as a double entendre.]
“To see some radiant nymph appear
In all her glittering birth-day gear,
You think some goddess from the sky
Descended, ready cut and dry.”
[A double entendre is possible, but I kind of doubt it. The OED seems to think so too; this particular section has four citations. Normally OED citations are in chronological order, the first two, which clearly refer to nudity, and the last two to clothing. The Swift cite, which appears third, is the earliest.]
1753 SMOLLETT Ct. Fathom II. xli. 43 He made an apology for receiving the count in his birth-day suit. [Probably yes.]
“...but hearing the count’s voice, he got up and opened the door in cuerpo, to the astonishment of Ferdinand, who had never before seen such a Herculean figure. He made an apology for receiving the count in his birth-day suit, to which he said he was reduced by the heat of his constitution, though he might have assigned a more adequate cause, by owning that his shirt was in the hands of his washer-woman.” [Clearly in the nude sense.]
1809 [see SUIT n. 19e]. (1809 MALKIN Gil Blas I. viii. {page}2, I will strip this holy father to his birthday suit.) [Yes]
[This one isn’t in Google Books, but I agree with Dr. T, it’s a reference to nudity.]
1727 SWIFT What Pass. Lond. Wks. 1755 III. I. 184 So many birth-day suits were countermanded the next day.[Probably not.]
“So many birth-day suits were countermanded the next day, that most of the tailors and mantuamakers discharged all their journeymen and women.” [Definitely not. And damn the OED for abbreviating the title of the essay to the point that it cannot be searched and damn Google Books for not making searches by volume possible. The full title is “A True and Faithful Narrative of What Passed in London.” I had a hell of a time finding this--I finally had to search author:Swift, title: works, word: countermanded in order to find it.]
1922 BLUNDEN Bonadventure xxvii. 167 A dancing saloon, where birthday suits were the fashion. [Probably yes.]
“Kelly was also of the opinion that Hamburg’s high place among towns was due to a dancing saloon, where birthday suits were the fashion.” [Kelly is a rather uncouth sailor, so it is certainly a reference to nudity.]