Frozen zombie mechanics

This may be a lil bit small, but can you add a mechanic where if the frozen zombie managed to get out of its snow cave/snow biome, they leave trails of snow, and when time goes by it will turn to a normal zombie, and also if Amy zombie entered a specific biome where it has its variations it turns into those, (husk in Dessert turning normal when left the biome) AND any zombie turns into that specific biome and variation. Plsss this would be great! Thank you