Sacrifices where the meat was not put on the altar will not have their hides given to the Kohanim. This is called olah ish, a sacrifice that is valid for a person. The hides of sacrifices offered without proper intent were still given to the priests. The hide is given to the kohanim whether it was brought by a man or a woman. The owners keep the hides of the less holy sacrifices and the priest keep those of the most holy sacrifices. In the case of a burnt offering, which is burned completely, the priests acquire its hide - the rabbis ask why they shouldn't receive the hides in all cases. The altar does not change anything for only the meat is burned on the altar.
It is notable that both women and men brought offerings. We know that women brought offerings after giving birth, which is specific to women. But other offerings brought by women were also valid. Prayer is understood as the modern stand-in for sacrifice. Bringing an offering in the proper manner with proper intent would be the same as actively leading prayer for oneself and/or a group of others. Wouldn't that suggest that women should be permitted to lead prayer?
Our daf ends with a second Mishna:
The hides of extremely sacred sacrifices are not given to priests if they were disqualified before they were flayed. They are burned together with the flesh. If they were disqualified after being flayed, their hides go to the priests. Rabbi Chanina was the deputy High Priest; he actually witnessed the Temple sacrifices, and he claims that he never saw a hid going out to the place of burning. Rabbi Akiva noted that Rabbi Chanina teaches that when one flays the firstborn offering and the animal later is found to be a treifa, the priests are permitted to sheye'otu, derive benefit, from its hide. The rabbis say that this is not proof; if after flaying the animal is found to have previously been unfit, the hide is burned.