I am familiar with the custom to immerse in a mikva for Shabbat, and also for Rosh Hashana and Yom Kippur. But is there such a custom for Passover?
The requirement to immerse in a mikva in preparation for the festivals is actually stronger than that for Shabbat.
The Sages thus taught (Rosh Hashana 16b), “A person is required to purify himself for the pilgrimage festivals”.
The reason for this special requirement of immersion for the festivals is that during the pilgrim festivals, every Jew had to go up to Jerusalem to appear before G‑d in the Holy Temple and partake of the sacrifices. This mitzva could only take place if a person was in a state of ritual purity.
Even nowadays when we do not bring sacrifices, the Sages still required immersion before the festivals so that we should imagine and desire that the Temple be rebuilt and feel ourselves prepared to fulfill the mitzva in purity. In fact, doing so is viewed as part of catalyzing the process. When G‑d sees our desire and anticipation to fulfill His will as in the Torah, He will hasten the Redemption and the rebuilding of His Glorious Abode.
Immersion in preparation for Passover is particularly apropos. Just as vessels are boiled, purged and purified in the mikva for use on this holiday of redemption, so too a person prepares himself for redemption on Passover by perspiring in performance of the mitzvot, purging himself of sin and shedding tears through teshuva and then immersing himself in the purifying waters of the mikva.