Would a consort be expected to do nothing more than bear children, or would she have significant power in the community? How much power could a countess have, upon the death of her spouse? Would a countess regular be appointed as regent for a child ruler?
As with many answers in history, the answer is frustratingly, "it depends." Depending upon region, legal precedent, common law, religious practices of the time, and the parties involved, medieval noble marriages could take many shapes and forms. For example, before he was king of England, John was Count of Mortaine and some other territories. He married Isabella of Gloucester and basically just put her in a tower. However, once he was king, he dumped Isabella of Gloucester and married Isabelle of Angouleme, who some chronicles label as "Helen" - blaming her for John's loss of his continental possessions because they were too busy feasting and fucking. After John died, she went back to Angouleme, but convinced her son, King Henry III, to haphazardly invade Normandy and try to take it back (spoilers: didn't work). With John, we see two very different roles that his consort had in his life. First, Isabella, is a non-factor who probably served as a way for him to get control of her dowry that came with its own money and lands. Second, Isabelle, who was crafty, manipulative, and seemed to convince the men in her family to make bad decisions. Now, if you look at someone like Eleanor of Aquitaine, the circumstances are different yet again. She controlled her own land, and bickered with both of her husbands over policy, financing, and administration (both of whom were kings, btw). But, Eleanor was an exceptional woman, especially with the emphasis put of patrimony in the Middle Ages. These are only a couple of examples, and there are many more that support, expand upon, and disagree with them. Someone who studies women in the Middle Ages will be able to provide you with a better answer.
So for a place to start, see
Elisabeth van Houts. Medieval Writings on Secular Women (2011)
Katherine Allen Smith and Scott Wells. Negotiating community and difference in medieval Europe: gender, power, patronage, and the authority of religion in Latin Christendom. (2008)
Jennifer Carpenter. Power of the weak: studies on medieval women (1995).
Hope this helps a little!