[From Rav Aviner's Commentary on the Haggadah]
Question: Why are women obligated in all of the Mitzvot of the Seder, when these Mitzvot are time-bound and women are exempt from time-bound Mitzvot?
Answer: They also experienced this miracle (Pesachim 108a-b). Here are two explanations for this answer. According to Tosafot, women are obligated because they were also in Egyptian Exile and were redeemed. According to Rashi, women are obligated because the Jewish People were redeemed on account of the righteous women of that generation. The first soldier in the struggle against Egypt was Miriam. "And I sent before You Moshe, Aharon and Miriam" (Michah 6:4). "You have three great leaders" (Ta'anit 9a). Miriam taught Torah to the women (Aramaic translation to Michah ibid.). She was born during the most difficult time for the Nation of Israel. She was therefore named "Miriam" based on the Hebrew word "Merirut" meaning "bitterness." The Egyptians decreed that every baby boy was to be thrown into the river. Amram, the leader of Israel, despaired and separated from his wife, Yocheved. He said: "Why should we bring more children into the world to be killed by the Egyptians?" The entire Jewish People followed his lead and separated from their wives. This would have certainly destroyed the seed of Israel and we would have been defeated without a fight. Everyone yielded except for one six year old girl – Miriam. She said to her father: "Your decree is worse than Pharaoh's. He only made a decree against the boys, but you made a decree against the boys and the girls!" She succeeded in convincing her father; he remarried his wife, and all Israel followed his lead and did the same. At the remarriage of her parents, Miriam danced with her little brother, Aharon, who was two years old. When Moshe was born, Amram was again concerned and wondered if perhaps he acted imprudently. Miriam, however, was confident that there would be a solution and, indeed, Moshe's salvation came in an unexpected way. Even before this event, Miriam showed herself to be a warrior. The Jewish midwives, Shifrah and Pu'ah, who saved the Jewish People, were Yocheved and Miriam. Even though Miriam was young, she helped her mother. Yocheved was called "Shifrah" because she made the child beautiful ("meshaperet" which is similar to "Shifrah") and cared for him. Miriam was called "Pu'ah" because she spoke ("Po'ah" which is similar to "Pu'ah), sang songs, and hugged him. When Pharaoh asked Yocheved why his decree to kill the baby boys was not followed, Yocheved evaded the question and said that the Jewish women are skilled at giving birth without a midwife. Miriam, however, spoke brazenly to Pharaoh, "She stuck out her nose at him and said: Woe to the man from whom G-d comes to take retribution. He was filled with anger against her and wanted to kill her. Yocheved attempted to pacify Pharaoh: "Do not pay any attention to her. She is a baby and does not know anything" (Shemot Rabbah 1:13). Miriam obviously understood everything, and she began to organize a rebellion ("Meri" which is similar to "Miriam") among the Nation of Israel. Our Sages relate how the women established a powerful underground in Egypt. They would encourage their husbands, give birth in the fields under apple trees, "I roused your love under the apple tree" (Shir Ha-Shirim 8:5), and raise their children in secret. They stubbornly continued to become pregnant and give birth, until they reached six hundred thousand. Including the elderly, woman and children, they reached a few million.
At a much later time, during the donations to the Mishkan (desert sanctuary), the women brought copper mirrors as a donation. At first, Moshe Rabbenu refused to accept them, since they were used to focus on the external beauty of women. "Grace is false and beauty is vain, a woman who fears Hashem, she should be praised" (Mishlei 31:30). Moshe was repulsed by the mirrors because they were used by the evil inclination. The Holy One, Blessed Be He, said to him: "Accept them, because these are the most precious to me.” Through these, the women created legions of Jewish children in Egypt. These mirrors were not objects of the evil inclination, but of the awe of Hashem. The daughters of Israel beautified themselves with them in order to entice their husbands who were exhausted from the back-breaking work. When Pharaoh decreed that the men would sleep in the field and the women in the city, the women heated up food and brought food and drink to their husbands. They would comfort them and say: We will not be enslaved eternally. Hashem will redeem us in the end. They took the mirrors, and each one would look in the mirrors with her husband and entice him with words…as it says, 'I roused your love under the apple tree,'" and this is how they had children. These mirrors are therefore called "legions of mirrors" ("Marot Ha-Tzovot"), because in their merit, legions ("Tzeva'ot") of Israel were born (see Rashi to Shemot 38:8).
Therefore, do not be surprised that after the splitting of the Red Sea, after the Song at the Sea of Moshe Rabbenu, "Miriam the prophetess, the sister of Aharon, took the drum in her hand, and all of the women followed her with drums and dances" (Shemot 15:20). They knew that the redemption was on account of their merit, the merit of the righteous women. They danced, they overcame the laws of gravity, they floated in the air, and they were freed from the physical reality of the land. When they left Egypt, they did not even bother to prepare leavened bread, yet they packed drums among their belongings out of the faith that a great salvation would occur and the chance would come to play music to the Master of the Universe, Redeemer of Israel.