Two Frozen Halves can be found in the Floating Catacombs. Her sprite is a palette swap of the Salem Witch with minor design changes, but the Frozen Half's attack patterns are more in tone with those of the Frozen Shade.
The player should be wise in making a priority dealing with them as soon as possible, as they can throw large chunks of ice at them or, in the worst case scenario, summon a freezing blizzard which covers almost the entire area (even if the room is many times larger than a single screen size), constantly knocking Alucard back while he receives cumulative heavy damage, and at the same time, preventing him from setting a foothold to counterattack.
Her voice also differs from that of the Salem Witch, which is understandable as the Frozen Half is in fact a transgender woman.
Further reinforcing this reference, she only appears in the Floating Catacombs, where Galamoth is indeed the boss of such area.
In the original release of Symphony of the Night, she is referred to as a "new-half ice spirit" in the enemy list's description, while in the Dracula X Chronicles version of the same game, she is referred to as a "transvestite ice spirit".
The Japanese word newhalf (ニューハーフ) is used to describe someone who is genetically XY and often has gone through hormone therapy and surgery to reconcile their body presentation with their internal gender. It is possibly the only in-game reference to transgenderism in both the Japanese and US versions of Symphony of the Night, and which is surprisingly retained in the latter.