Notwithstanding the diversity of the various peoples we'd consider as Ancient Celts (e.g. peoples of Gaul, Britain, Ireland, Spain, etc.) whose customs could be as similar as they'd be different, I'd like to focus a bit on the warring and military functions in Iron Age societies in Britain and especially in Gaul; whereas I'd like to thanks u/Kelpie-Cat for what she wrote about the status of women in ancient and early medieval Ireland For instance, there's no really mentions of women of these societies as warriors or fighting as the warriors-aristocrats would do.

Not that they wouldn't ever take part in fighting at all : migrations, sieges or even mercenariate, where conflicts would necessarily involve women (as well as people unfit to fight, children or elderly) whose fate was immediately on balance, which in defeat meant assault, slaughter or enslavement. An almost systematic trope in Caesar's De Bello Gallico is describing women begging for the victor's clemency and being spared this, but we have as well some mention of women taking an active part in fighting, leaping into battle with whichever weapon they found when warriors failed to hold on as described for the Battle of Aix (Plutarch; Marius, XIX) or while not fighting, putting themselves in danger while encouraging warriors to commit to the battle (see the previous exemple, but as well Caesar; DBG I, 51 and VII 26 and 58 or Tacitus; Annals, XIV, 30), sometimes up to share their fate as men, killed or killing themselves to be spared the consequences of defeat : this could explain that among the ossuary of the sanctuary of Ribemont s/Ancre, generally held to be a trophy erected at the place of a battle, one third of these remains are considered to be women's.

Feminine bravery isn't debatable, being a trope of ancient litterature evocating admiration and repulsion of the authors at the mention of dishevelled and fierce women, but these appear to be contextual at best whereas other sources mention them in the lot of non-fighters, counted along non-fighters in the Helvetii cens tablets (DBG; I, 29). As the warrior function was a celebrated social and religious public status, it also seem it had to met a set of expectations, rites and displays that exlucded these non-fighters as a whole and women in particular : pederasty, clear distinction of the familial and public sphere with men being active participants (DBG; VI, 18) or the participation to assemblies in arms (Livy; XXI-20)

Eventually, Late Iron Age funeral deposits don't provide evidence of women as warrior, whereas weapons are systematically associated with masculine graves, funeral display or art in general (e.g. the guerrier de Saint Maur, coins bearing masculine names as this one with the name LUCIOS but further in Europe the warrior statues of the Castro culture, the Braganza Brooch, etc.

I'm not privy to future archaeological discoveries or reinterpretations (something comparable to the corrected assessment of the Bj 581 grave of Birka, containing the remains of a woman with deposits of weapons and not a man as previously thought?), but what's at disposal certainly seems to point that, while nothing absolutely prevents the possibility of women having fought as warriors, that'd would have been exceptional and outside the gendered and social norms and expectations.

The idea of women having an equal position in Celtic society is an exaggeration, mostly borne from Boudicca being mythologised as a British cultural symbol of independence. While they were better off than their Roman counterparts, Celtic women still lived in a patriarchal society.

First, some context on Celtic women in general. Like in Rome, Celtic husbands had the power of life and death over their wives, although, also like in Rome, this was rarely put to the test. Furthermore, political marriages were as common among the Celts as they were with the Romans. In contrast to Rome, where men controlled all family finances, Celtic couples would pool an equal amount of money when married, and the surviving spouse would get the full amount upon their partner's death, regardless of sex. From this we can presume that Celtic women had much greater autonomy than Roman women, at least financially. Celtic women also had more latitude to work in a skilled trade than Roman women, although metalworking was restricted to men. The Celts were also known to practice polygamy, although it was much more common for men to take multiple wives than vice versa.

Now on to the battlefield! The idea of Celtic warrior women taking to the field to fight alongside their men is a misunderstanding of Classical sources of the Celtic migrations that mostly took place in the 300s B.C.E. The 300s were a period of overpopulation in traditionally Celtic land that caused mass movements to colonise non-Celtic land. Most notably, the Celts moved into northern Italy and Greece. For the Celts, it was a process of relocation that involved moving entire families, including women. For the Italic and Hellenic peoples, it was not-unreasonably considered an invasion, and was thusly responded to with force of arms. While there are very few accounts of Celtic women actively taking part in fighting, their presence on the battlefield gave the impression that they were combatants, while in reality the entire migratory Celtic community was present on the battlefield in a non-combatant capacity.

This lastly brings us to Boudicca. We know for certain that Boudicca led the Celtic Iceni and Trinovantes tribes in rebellion against Roman rule in 60 or 61 C.E. The Iceni had been allies of the Romans, and upon the death of their leader and Boudicca’s husband, Prasutagus, the process to integrate the Iceni into the Roman Empire began. This was done with remarkably brutal incompetence; Boudicca was flogged and her daughters were raped by Roman functionaries. This triggered Boudicca’s famous rebellion, which ultimately ended in failure and her likely suicide. Boudicca is often depicted as a warrior queen, but her leadership of the rebellion was more than likely symbolic as a Celtic woman trying to restore the dignity of her society. We can surmise that Boudicca was very much an outlier as a Celtic woman ruling on her own.

Sources:

Green, Miranda J. The Celtic World (London: Routledge, 1996).

James, Simon. The World of the Celts (London: Thames and Hudson, 1993).