Did they still go into battle naked and painted blue circa 60 CE?

There's several possible misconceptions there : keeping in mind that "Celtic" tends to lumps together geographically and chronologically distinct peoples, and that a lot of descriptions of ancient "Celts" are often description of Gaulish situations (although that Gaulish and British cultures seems to have been close enough, at least in languages and basic practices)

First, while Gaulish or British women could have an important and influential social role, to the point they could effectively if not legally lead peoples or coalitions as did Boudica, that was the rare exception.As for warfare, there's no evidence that British or Gaulish women participated to regular warfare, neither trough an historical mention, neither trough archeological discovery.There's however a possible exception with women accompanying mercenaries or moving with them during a migration : there's some feminine graves in Northern Italy possibly associated with or neighboring warrior grave (would it be only as "guarantee" of her spouse or concubine's prowess). With the there's the example of the Battle of Vercellae^(1) against Marius' troops^(2) with women being part of a desperate defense or a last ditch without being fighters, something which wasn't particular to Gauls in the Mediterranean world ( Pyrrhos having got the point when he got the brick).

This is not to mean that women didn't played an important social and political role, including in military matters. : in Gaul, they could participate to assemblies (keeping in mind presence was largely dictated by one's social and military status), that is public political life, about deciding of war and peace; or dispute among allies.In addition to aforementioned graves, there's the presence of feminine remains where warriors would be expected and there's a possible case at Oleggio of an incinerated ruling woman (REIKNAS, queen?, being written on a plate of the grave) with weapons as a power display : while there's strictly no indication of Gaulish women being part of regular fight (an activity supremely associated with virile virtues), they might not have been put aside from the war in a general sense even if Agricola's account of Boudicca have her first justifying to the assembly of her leadership, meaning that if the practice existed in Britain as well, it wouldn't have been necessarily expected.^(2)

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The naked Celtic warrior was first a Greco-Roman trope that knew an important diffusion in Antiquity, before becoming a romanticist myth. There's little truth to the first, and none to the second (essentially as the XIXth century saw "Celts" as essentially interchangeable people with IInd century BCE Gaul being the same as the VIIIth century Scot).

It comes from Polybus and Titus-Livus, the first describing a troop of Gaisates (Gaulish mercenaries) fighting Romans in Northern Italy, or rather, describing the first line of their armies while taking note the other had a better protection; the second accounting for naked Gauls at Cannae at Hannibal's side. Caesar for the Gallic Wars, or Agricola for the campaigns in Britain, never mentions it, still, as any other Greek or Roman author.What does this nudity uncovers?^(4)

Well, it might be a matter of equipment than being au naturel , describing troops without armor but having long spears on hand or swords hung on iron chains while still having their bracatae on (or probably rather sort of leather skirt, reinforced or not by metal), such as described by Plutarch ("almost naked and lightly armed"). Front lines being thus light on their foot and able to quickly jump on their enemies, or riding and thrusting them.

It doesn't mean that Gauls didn't sometimes fought in their birthday suit in order to impress both friends and enemies (and possibly the divine) with virile display and endowment; but that wasn't regular and "naked" might even there mean warriors proudly showed off their chest in defiance with little to no defensive armament.

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The use of blue dye among Brittons is rather complex, and seems to have been gendered in its use : while Caesar describe southern British people adorning a blue dye for war, Pliny rather indicate that women used this dye (probably imported from Gaul) used it to mark their marital status5. It is possible that northern Brittonic peoples such as Calidones and Uotadinii (eventually being part of the broad coalition later known as Pictii) did likewise, although it might be in a different way (possibly using metallic tincture from cooper).

As such it wouldn't be wrong to depict Boudica with a blue-ish color (possibly dark blue-green), but maybe entirely so rather than with henna-like decorations.

^(1) Cimbric, Teutonic and Ambronic peoples involved being likely a mix of Celtic and Germanic groups and elements.

^(2) Florus, Epithome, 38

But the struggle with the enemies' wives was not less severe than that with themselves; for the women, being mounted on wagons and other carriages, which had been ranged around as a defense, fought from them, as from towers, with spears and pikes

^(3) Tacitus, Agricola,

Boudicea, with her daughters before her in a chariot, went up to tribe after tribe, protesting that it was indeed usual for Britons to fight under the leadership of women. "But now," she said, "it is not as a woman descended from noble ancestry, but as one of the people that I am avenging lost freedom, my scourged body, the outraged chastity of my daughters. Roman lust has gone so far that not our very persons, nor even age or virginity, are left unpolluted. But heaven is on the side of a righteous vengeance; a legion which dared to fight has perished; the rest are hiding themselves in their camp, or are thinking anxiously of flight. They will not sustain even the din and the shout of so many thousands, much less our charge and our blows. If you weigh well the strength of the armies, and the causes of the war, you will see that in this battle you must conquer or die. This is a woman's resolve; as for men, they may live and be slaves."

^(4) I'm not ashamed of the puns, that's the naked truth.

^(5) Pliny, Natural History

In Gaul there is a plant like the plantain, called glastum; with it the wives of the Britons, and their daughters-in-law, stain all the body, and at certain religious ceremonies march along naked, with a colour resembling that of Ethiopians.