In the debug screen (f3), when you are in a frozen ocean chunk, the name is displayed as "FrozenOcean", unlike the Lukewarm Ocean. This is probably a bug (easy fix!).
EDIT: This problem also occurs in the "FrozenRiver" (Frozen River) biome.

Seed: 1
FrozenRiver: /tp @s -1641, 63, -290
FrozenOcean: /tp @s -2049, 63, 874

Seed: -8300275442758179407
FrozenOcean?: /tp @s -875, 85, 228