that’s an excellent question, nonnie. and the answer is not simple — as putting a label on ‘intelligence’ in general is a problematic task. there are many facets and faces to intelligence, some at which she excels and some of which she may fall short in. when starting off this discussion, i think it is firstly important to outline some very wide headcanons that i have for rohirric culture in general.
as we know from the texts, the éothéod have a strictly oral culture. rohirric has no corresponding alphabet apart from a few basic conveyant runes. the language is not written and the people of rohan do not record their history in texts. while we know that they do record great historical figures using the textile arts ( as in the great tapestries that decorate meduseld ), it is mostly in song ( and some story ) that their tradition is maintained. cultures with oral traditions are fascinating in general but what i like to keep closest at heart is the understanding of the transient nature of history that it imparts upon the people who participate within such a tradition. the rohirrim, as i see them, are not a people deeply concerned with ancient history, either their own or that of other cultures. stories that DESERVE to be told will be remembered, such songs beloved, but they embrace the idea that some stories and songs fade with time when they are no longer powerful and no longer relevant. this is the way of things. the intensive study of ancient things, to them, is ponderous and useless. they live very much in the present, in temporal things. being not long removed from their nomadic past, survival and stewardship, the basic and brutal, are more the heart of their culture than arts and ‘higher’ educations.
these headcanons that i hold have a strong and obvious correlation to éowyn’s intelligence in the limited context of pure education. in this regard, she could be called ignorant. contrary to the non-canon exchange with aragorn in the films ( in which she describes the dúnedain as descendents of númenor ), in the novels she has no knowledge of númenor when faramir mentions its doom to her. thereby we can assume she knows little of the history of gondor past the recent. it is my headcanon that the education of the royal line in rohan is concentrated more in their roles as military leaders, since the ‘elite’ of rohan are more directly tied to practical ruling and defence than any philosophical role. military history and tactics, an understanding of ethical law, and the great deeds of the line of kings. the goal of their education is in the ruling of farmers and herdsmen and warriors, and is therefore of a more practical nature.
éowyn is not well educated by southern standards, or by standards that any firstborn may hold. she is, in fact, to be counted quite ignorant in such regard. though naturally curious, she simply has been taught to place a low value on scholarly pursuits. after all — when she first meets faramir she is not impressed by his intelligence or any idea of his reputation as a great scholar, but by the look of him as a great warrior. ‘she having been raised by men of war’, is the quote, i believe, that describes her worldview. we know from her dialogue and the descriptions of her that she is a keen judge of people and situations and that she has a quick wit and can express herself quite powerfully. these are all qualities that i try to maintain in my portrayal — because this is the measure of intelligence that is most relevant to her and to her cultural context. she IS very intelligent but she is NOT learned in a scholarly sense.
for example : though she knows nothing of the history of numenor, she clearly has a great knowledge of war. she is able to, single-handedly ( in command ) and with no warning, organize the muster and layout and establish a camp housing most of rohan’s troops and all the necessary equipment and provisions in less than a week. no dummy is gonna pull that off. she is clearly a capable ruler and commander, a quick wit and a skilled orator. however, put a quill in her hand and she would struggle to remember the written westron that she was taught as a child ( westron being the court language of rohan ), for she has so little use for it. her handwritting may be crude and childish, it may cause a gondorian noble to snicker when reading any letter that she would struggle, but in the context of her own people she is indeed a great force to be reckoned with and it is my headcanon that her natural wit and curiosity combined with her fierce determination would enable her to be quite the scholar as well — had she the will / interest and a capable teacher.