From the Super Mario Wiki, the Mario encyclopedia
Super Mario 64 / Super Mario 64 DS
In Super Mario 64 and its remake, Super Mario 64 DS, freezing water appears in Snowman's Land in two forms. The first type of water cannot be touched at all, and any character who makes contact with it loses three wedges of health and bounces away, in a similar manner to lava. This water is only found in a large pool underneath the Chill Bully's platform. When pushed off, the Chill Bully will melt in the freezing water and be defeated.
The second type makes up the freezing pond and acts much like regular water; however, this water is so cold that the player will begin to lose a wedge of their Health Meter for every two seconds they are in it, and will not recover health automatically like in regular water.
Super Mario Galaxy
Freezing water also makes an appearance in Super Mario Galaxy in the Freezeflame Galaxy. Like regular water, it can be swum in; however, if Mario or Luigi stays in it for too long, they will lose one slice of their Health Meter. Therefore, to traverse it, an Ice Flower is required. When jumping into this water, the screen will "tingle" for a split-second.
There is a exploit that allows Mario or Luigi to traverse freezing water without using an Ice Flower or taking damage over time. Usually, Mario or Luigi can not jump in water unless they are next to land. However, a second player utilizing the Star Cursor can make Mario or Luigi jump, even if they are in water. Jumping out of the freezing water immediately cancels the code for taking damage in water. This means that if the second player makes Mario or Luigi jump consecutively within around 2 seconds of each jump, Mario or Luigi will safely be able to swim across freezing water.
Super Mario Odyssey
Freezing water can be found primarily throughout the Snow Kingdom, as well as a bonus area in the Sand Kingdom in Super Mario Odyssey. If Mario swims in it, the screen will gradually become covered with frost, and if he stays in too long, he will take damage. He can avoid taking damage from the freezing water by capturing a Snow Cheep Cheep. Gushens can also travel safely across freezing water. One area of the Darker Side course also features a moving block of freezing water, through which Mario must swim to avoid a set of Fuzzies.