The Carneia pops up a lot in the activities of the Spartans. They used it to excuse their absence at Marathon. Less famously but probably more importantly Herodotus 7.206 tells us that the reason the Spartans only sent a token force to defend the pass at Thermopylae was because the Carneia was going on. The Spartans weren't the only ones: the same passage says that the other allies were celebrating the Olympic festival, so the full levies of the allied force were not available for Thermoplyae, only small forces that each city was able to send. That seems questionable. The allies had already advanced past the Thessalian plain and then fallen back past it at the behest of Alexander, which according to Herodotus they justified later by saying that there was an alternate pass into Thessaly that the Persians ended up taking anyway. Similarly, the Athenians had no qualms with mobilizing their entire fleet to Artemisium at the same time, Olympia or not. And given the well-known Spartan and Corinthian hesitation in Book 8 of Herodotus to march past the isthmus during the war against Xerxes, the Carneia seems too convenient an excuse. Herodotus suggests as much, saying at 7.206 that the Spartans sent Leonidas' small force forward to keep the allies in the north from medizing ἢν αὐτοὺς πυνθάνωνται ὑπερβαλλομένους "if they learned that the Spartans themselves were putting the campaign off." Literally ὑπερβάλλω means "to throw over," but idiomatically in context it means to kick things down the road, as it were. The Carneia got in the way of Spartan military affairs, or was used by them as an excuse to go home, at least one other time. Thucydides 5.54 mentions that when the Spartans marched against the Argives they found the omens unfavorable and disbanded the army, commanding the allies to reassemble in two months, since the next month was Carneus, when the Carneia was supposed to happen. Here Thucydides tells us that the month was sacred to all Dorians, though I don't know of anyone other than the Spartans ever having an issue with military activities during it. Thucydides 5.75 says that after their victory the Spartans ordered the allies not to go past the isthmus in pursuit of the Athenians and went home for the Carneia. He also mentions that the accusations against the Spartans that they were cowards, old-fashioned, or sluggish in the war, which has been a major theme in Books 1-4, were dispelled by their behavior in this battle, but of course Thucydides also says this immediately after describing how the Spartans forbade their allies from following up on their success and went home for religious observance, precisely the sort of activity that in previous books of Thucydides has caused the Spartans to be called unadaptive and behind the times. It seems to me hard not to understand him as being heavily ironic. The same passage also has Thucydides mention three thousand Eleans (also Dorians) marching to Epidaurus under the command of the Athenians to attempt to circumvallate the city while the Spartans were at the Carneia. Apparently the Eleans didn't have the same issue, even though Thucydides says that all the Dorians consider the month of Carneus holy.