The Cold cow's texture layout is different from the Temperate and Warm cow, the snout texture is in a different position.

Similarly, both the Pig and Cow variants, despite all being the same mob and sharing the updated 64x64 texture size, do not share their features between each other. If you try to use the "coat" layer from the cold pig or cow on the temperate or warm versions, the coat layer does not render. Similarly, you cannot use the unique horn shapes of each cow variant for any of the other variants. 

To me, this seems like a bug since they all share the 64x64 texture layout. It seems weird that their models would be updated but not be usable between the variants, particularly for resource pack makers.

How to reproduce:

1. Download the test resource pack to your resource pack folder
2. Start game in the latest snapshot (25w05a)
3. Enable the resource pack from the menu
4. Summon the mob variants using the commands below
5. Observe

/summon cow ~ ~ ~ {variant:cold}
/summon cow ~ ~ ~ {variant:temperate}
/summon cow ~ ~ ~ {variant:warm}

/summon pig ~ ~ ~ {variant:cold}
/summon pig ~ ~ ~ {variant:temperate}
/summon pig ~ ~ ~ {variant:warm}