Women, despite being exempt from certain time bound positive commandments, are obligated to make kiddush on Shabbat. My question is, are women also obligated to make kiddush on Yom Tov or no? And can they fulfill a man’s obligation?
There are definitely sources that show that women do have an obligation.
Like @JoelK mentions it is discussed in Shu"t Rabbi Akiva Eiger, Mahadura Kamma #1. He writes there:
רוב נשי דידן מחמירין לעצמן וזהירות וזריזות לקיים רוב מ”ע שהז”ג, כגון שופר סוכה לולב וכן בקידוש יום טוב והוי כקיבלו עלייהו
The majority of women are strict on themselves and are careful and zealous to fulfill the majority of positive time-bound commandments, such as shofar, sukkah, lulav, and similarly kiddush on Yom Tov, and it is as though they have accepted it upon themselves [as a binding custom].
In a similar vein, the Minchas Chinuch 31 writes that they would be obligated if viewed as Torah rather than Rabbinic obligation:
בקידוש י”ט אי נימא שהוא מה”ת אפשר שהוא שוה לשבת גם לענין נשים שחייבים אך אם נימא שהוא מדרבנן אפשר דאין נשי' חייבות…
With kiddush on Yom Tov, if we say that it is obligatory on a Torah level, it is possible that it is equal to Shabbos also regarding women, that they are obligated. But if we say that it is of a Rabbinic level, it is possible that women are not obligated…
Finally, note the Shulchan Aruch HaRav OC 271:4 who also notes that Yom Tov is similar to Shabbos, and just as the women have an obligation there, so too they have by Yom Tov.
הַקִּדּוּשׁ בְּיוֹם טוֹב הוּא מִדִּבְרֵי סוֹפְרִים,כג וְאַף עַל פִּי כֵן יֵשׁ לוֹ כָּל דִּינֵי קִדּוּשׁ שֶׁל שַׁבָּת לְכָל דָּבָר.
[The recitation of] Kiddush on a festival is a Rabbinic ordinance. Nevertheless, all of the laws that apply to Kiddush on Shabbos apply to it in every regard...
He then continues in the following se'if:
נָשִׁים חַיָּבוֹת בְּקִדּוּשׁ הַיּוֹם בְּשַׁבָּת מִן הַתּוֹרָה, וּבְיוֹם טוֹב מִדִּבְרֵי סוֹפְרִים. וְאַף עַל פִּי שֶׁכָּל מִצְוַת עֲשֵׂה שֶׁהַזְּמַן גְּרָמָא נָשִׁים פְּטוּרוֹת מִמֶּנָּה – בְּקִדּוּשׁ הַיּוֹם חַיָּבוֹת, שֶׁנֶּאֱמַר "זָכוֹר אֶת יוֹם וְגוֹ'", וְנֶאֱמַר "שָׁמוֹר אֶת יוֹם וְגוֹ'", כֹּל שֶׁיֶּשְׁנוֹ בִּשְׁמִירָה יֶשְׁנוֹ בִּזְכִירָה
Women are obligated in the sanctification of the Shabbos day according to Scriptural Law and in [the sanctification of] the festivals according to Rabbinic decree. Although women are exempt from all positive commandments that are dependent on time, they are obligated in the sanctification of the [Shabbos] day. [This concept is derived as follows:] It is written: “Remember the Shabbos day to sanctify it” and it is written: “Observe the Shabbos day….” [Our Sages stated:] All those who are obligated to observe are obligated to remember...