Answer: The Shulchan Aruch (OC 503:1) writes that one mustn’t prepare on Shabbos or Yom Tov for the following day, even if that day is Shabbos or Yom Tov. Thus, one mustn’t wash dishes on Shabbos or Yom Tov that won’t be used that day (ibid. 323:6).
The Mishna Berura (667:5) writes that this issur even applies to preparing for mitzva purposes, such as rolling a sefer torah for the next day’s leining.
The Mishna Berura (ibid.) quotes the Chayei Adam (153:6) who allows one to bring water or wine from a storeroom during the daytime while it’s still light for the following night. One should do it earlier in the day, however, to not make it too obvious to others that one is doing so for the following day. The Chayei Adam, writes, however, that this specifically applies to something needed for a mitzva such as a Yom Tov meal.
Similarly, the Magen Avraham (OC 500:13) and Shulchan Aruch Harav (OC 500:20) write that one may soak raw meat on Yom Tov on the third day of it being shechted so that it can be properly salted afterwards. If one leaves the meat, it will be too late to wash it. Unlike washing dishes for the following day which is prohibited as one is actively performing something, soaking meat does not involve any substantial action.
Based on this, R’ Ephraim Greenblatt and R’ Gavriel Zinner (Rivevos Ephraim 3:268; 4:248) write that one may remove frozen food from the freezer, writing that moving the food does not constitute an action of hachana (See Machazeh Eliyahu 1:64:35).
While R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 10:10; n27) writes that one mustn’t remove food from the freezer on Shabbos or Yom Tov for the following day, he writes that R’ Shlomo Zalman Auerbach deliberated whether this is similar to washing dishes or not.
In conclusion, one may remove food from one’s freezer on Shabbos or Yom Tov, especially for another Shabbos or Yom Tov meal, though one should do so in an inconspicuous manner.