Rabbi Joseph Hayyim, Rav Pealim, Yoreh Deah 1:44

Question And furthermore he [the penitent sinner] asked [R. Joseph Hayyim] about the healing-atonement (tikkun) for lying with a man. Our teacher the ARI [R. Isaac Luria] of righteous and blessed memory wrote that he should fast two hundred and thirty-three fasts and roll in the snow. The student wanted to know, if he fasted in the winter two hundred and thirty-three fasts expecting to roll in the snow during this time [but could not because] in the end there was no snow, would it help to roll in the snow later when it was available, or was he required to roll in the snow during the fasts? Moreover, he asked, if the tikkun of rolling in the snow worked even after the fast period, then perhaps the fasts alone were enough? Also, what if the snow had melted in one place and become water and he bathed in it, would this be sufficient or not? Answer It is explicit in the words of the ARI, of blessed memory . . . that the snow tikkun must be during the fasts. However, if he does not perform the snow tikkun during the fast days, but on another day, without a fast, he did perform a tikkun for the sin, but it is not a complete tikkun . . . Here, where there was no snow, and he only performed the fasts, he is certainly constrained, and The Merciful One cares about a person's intent. Since this person carried the great burden of these fasts, the entire world can see that if he had access to snow, he would have rolled or immersed in it, and therefore God will certainly consider it as if he had done the complete tikkun. Nevertheless, it would seem to me that he should try to find at least a piece of ice during his fast days. [A piece whose] size would allow him to roll his hands in it from his finger tips to his shoulders, front and back, nine times. A piece like this you can find in the winter, since if you place a bowl with a little bit of water on the roof at night, by morning the water will become a piece of ice. . . And with regards to the question, if immersing in melting snow counts, it is explicit in the words of Our Teacher, of blessed memory, that it works. . . However, note that he should immerse in it when it is still very cold, and not after it warmed up, and the strength of the cold left it, since the secret of the tikkun is dependent on that he immerses in the snow while it is still very cold, so that his body cools down . . . [Translation by Rabbi Steven Greenberg]