The Rambam (end of Hilchos Ta’anis) writes: “All these fasts in the future will be nullified in the days of Moshiach, not only that, but they will turn into ימים טובים וימי ששון ושמחה – Yomim Tovim, and days of celebration and joy. Like it says (Zechariah 8:19): כה אמר ה' צבקות צום הרביעי וצום החמישי וצום השביעי וצום העשירי יהיה לבית יהודה לששון ולשמחה ולמועדים טובים והאמת והשלום אהבו - So says Hashem the Lord of the Hosts, the fast of the fourth (month,17th of Tammuz), the fast of the fifth (month, Tisha B’Av), the fast of the seventh (month, Tzom Gedalyah), and the fast of the tenth (month, Asorah B’Teves), shall be (changed over) for celebration and joy for the household of Yehudah, and good times, and truth, peace and love.”
R' Shmuel Hominer (cited in Moriah, Year 7, Gilyon 6, pg. 41) is in doubt, if when the Rambam writes: עתידים להיות ימים טובים – “In the future they will be Yomim Tovim”, if the Rambam means a real Yom Tov like Shavuos, or if he perhaps he means a Yom Tov like Purim. The practical difference would be, if the fast would fall out on Shabbos: If it is a real Yom Tov then even if it would fall on Shabbos we would make a Yom Tov/Shabbos seudah on Shabbos, if, however, it is a Yom Tov like Purim, then we would push off the seudah until Sunday (like what we do when Purim falls on Shabbos).
His doubt seems to come from the fact that the Rambam changes the lashon of pasuk. The pasuk in Zecharia says, ולמועדים טובים, however, the Rambam writes, ימים טובים. From the pasuk it seems like it would be a proper Yom Tov, however, from the lashon of the Rambam ימים טובים, it seems that perhaps the Rambam learns that it won’t have the status of a Mo’ed, where it is forbidden to do melachah, rather it will have a status like Purim where we find in Megillas Esther (9:19) that is referred to as שמחה ומשתה ויום טוב – “a day of happiness and feasting and a Yom Tov”, and Purim is not completely like a Yom Tov, and one is allowed to do melachah.
If in the days of Moshiach, Asorah B’Teves will be a proper Yom Tov, and not just like Purim, then when it falls on erev Shabbos like this year, there is room to doubt if perhaps one is obligated to make an eruv tavshilin on Thursday, in order to allow cooking on Asorah B’Teves for Shabbos. Although the Gemara in Eruvin (43a) teaches: “There is a guarantee that Eliyohu HaNavi won’t come on erev Shabbos, and erev Yom Tov due to great effort (Rashi explains, people will have to leave Shabbos preparations and greet Eliyohu HaNavi)”, therefore, there is no reason to worry that he will come when Asorah B’Teves falls on erev Shabbos. The Chasam Sofer already says, that just like Eliyohu HaNavi will answer all the תיקו’s, unresolved questions in Shas, similarly, if he comes on erev Shabbos he will have an answer as to how it was possible.
Consequently, since he can come on erev Shabbos, perhaps there is room to say that one should make an eruv tavshilin, at least without a berachah, on Thursday the 9th of Teves this year, so that one will be able to cook on Asorah B’Teves for Shabbos.
