I was playing on my survival world looking for the new wolf types, but I kept seeing the old wolves spawn in biomes where they were supposed to have different skins. For example, in the forest biome, Woods wolves were not generating, but the old ones were. I decided to hop onto my creative world, and it demonstrated the same issue. However, when I spawned wolves in using eggs and commands, they were generated with the correct skins. This issue only happens in older worlds. Both of the worlds I noticed this on were from 1.19. New worlds do not seem to have this issue. I decided to try one more thing, and in my creative world, teleported myself 200,000 blocks out. I did this to find raw chunks that hadn't been generated yet, and I saw the new wolves spawning naturally. 

TL:DR New wolves only spawned after going to new chunks in old worlds.