Some Ahadith seemingly mention that a woman's power of reasoning is less than that of a man and that women are less sensible than men. Is that so?
I am afraid that this is a wrong conclusion. It has arisen because of a wrong translation. Here is a correct translation of one of the texts reported by Abū Saī‘d Khudrī:
[The Prophet (sws) while talking to a group of women once said]: … and I have seen you rob even a wise man of his senses in spite of being given relaxation in worldly affairs and religious affairs, They said: O Allah’s Messenger, what is this relaxation? He said: Is not the evidence of a woman equal to half of a man’s. They said: Yes. He said: This is the relaxation given to them in worldly affairs. He said: Is it not a fact that when they enter the period of menses they neither observe prayer nor observe fast. They said: Yes. Whereupon he said: This is the relaxation given to them in religious affairs. (Muslim, Kitāb al-Imān)
The Arabic phrase Nāqisāt al-`Aql wa al-Dīn has generally been translated as “faulty” keeping in view the Urdu meaning of the word. However, in Arabic, the verb Nāqasa means "to reduce" and the correct translation of the above phrase, if the context is also taken into consideration, is that women have been given a relief and reduction in their worldly and religious duties.
The relief in worldly responsibilities, as is mentioned in this Hadīth, is that women have not been dragged in certain activities and spheres. For example, the Qur’ān urges men to testify on legal documents so that women are relieved of appearing in courts and wasting their precious time on affairs which others can handle. Only if men are not available should a society involve women in such affairs.
The relief women have been given in religious affairs is that they are not required to pray or fast during their monthly periods as is mentioned in this Hadīth.