The question in the title, in some ways, ought to be an unnecessary one. Even in 1981, when Suzanne Wemple was claiming they didnt, it needed a very narrow definition of the movement to exclude them. If the hagiographer Hugeburc gets excluded because her education was Anglo-Saxon and she didnt write in the ninth century, then youre also left with a Carolingian renaissance sans Alcuin. And to imply that Dhuoda doesnt count because shes a laywomen is ridiculous. Ever since the evidence has been pointed out for womens involvement in the movement. Rosamond McKittericks written on female readers and scribes, Jinty Nelson on female historians, Steven Stofferahn on nuns and learning and many others.
The more interesting question, perhaps, is what kind of Carolingian renaissance did women have? Here, I want to focus more on the intellectual than the moralistic side of the renaissance and compare it with two other periods: late antiquity and the twelfth century renaissance. One interesting way in is to start with the question of what women are reading in the period and what are they writing?
As far as the reading goes, it looks like pretty much everything that men were reading. History, hagiography, poetry (Dhuoda knows some Ovid), theology, medical books and even law texts (one of Eberhard of Friulis daughters gets a copy of the Lombard laws). Theres also at least one mention of a text in German. The writing is harder to be certain of, but presuming that the Earlier Metz Annals were written at Giselas command (which seems plausible), we have history, hagiography, moral/political tracts (Dhuoda), poetry (Dhuoda again, and nuns songs) and letters. (In fact, the Carolingian world may possibly be the first time in Europe/Mediterranean that women are writing history at all (though if somebody knows better, then let me know), whereas theres earlier hagiography, poetry and letters by women).
What we dont have, as far as I know, is women writing academic theology, philosophy/science or law and what is interesting is that those three categories look fairly constant over most of antiquity and the Middle Ages as well. Of the three categories, two seem rather obvious exclusions. Women were largely excluded from the law courts, so were unlikely to be able to discuss the topic. And I imagine that academic theology/biblical exegesis, even before it got confined to the universities, would have been seen as too much like women teaching, and fallen foul of St Pauls views. (Mystical theology by women, in contrast, seems to have been regarded as OK). As for why no philosophy or science, thats slightly trickier, but I suspect thats to do with how it was taught. More than theology (which you could do off on your own with a collection of the key texts), philosophy tended to be taught personally in a master-disciple relationship, up till the late Middle Ages, at least. Women could only really gain access to this process via close family connections (to avoid scandal): most of the ancient Greek female philosophers seem to have been daughters of male ones. Once philosophers could have neither wives nor daughters, that way in was largely blocked. In addition, philosophy and other sciences relied more than other subjects on getting hold of new texts: the study of both logic and grammar in the Carolingian renaissance were crucially influenced by texts that Alcuin brought to the Continent. Womens access to new texts (in terms of material resources in nunnery libraries, and the opportunities to seek out new manuscripts) were always going to be a disadvantage for them in such spheres. Its also possible that thats why the greatest early medieval religious women writer, Hrotsvita, wrote in the tenth rather than the ninth century; because it took longer for nunneries than monasteries to benefit from the boost to learning that the Carolingian renaissance gave. (Rosamond McKitterick has pointed to patterns suggesting female scriptoria being built up, with nunneries which have books copied elsewhere in the ninth century, then copying their own in the tenth century).
What all this suggests is that women had about as much of a Carolingian renaissance as it was realistically possible for them to do at the time. Its hard to see many institutional changes that allowed Ottonian nuns to write and prevented Carolingian ones from doing so. Strict claustration and nunneries not being allowed to educate boys, which Wemple focuses on, wouldnt, to my mind, be likely to make a major difference. And as Katrien Heene has pointed out, theres not much sign of Carolingian men thinking intellectual activities are unsuitable for women. Religious women didnt achieve/benefit as much as religious men in the renaissance largely because they were starting from a lower educational and material basis. Meanwhile, laywomen seem to have shared as fully in the renaissance as laymen. In particularly, its not just the existence of Dhuoda, that suggests this, but that we dont know her family background. Unlike Heloise, unlike Radegund and Christine de Pizan, she didnt (as far as we know) receive an unusual education from an intellectual family (and I bet she didnt get it from Bernard of Septimania). Compared to the twelfth century and its institutional and linguistic barriers to female learning (the university and Latin) and to late antiquity and its traditions of public schools, the Carolingian period appears to have been relatively more favourable for womens intellectual activity. The fact that still meant that they couldnt participate equally in the renaissance shows how deep the structures ran that limited female opportunities.