Wither Skeletons brought to the Overworld via Nether Portal will attempt to hide from daylight by seeking shade or water. This is due to the fact Wither Skeletons share the same entity ID as Skeletons.
Steps to Reproduce:
1. Make a new Creative world.
2. Create the structures show in the pictures.
3. Construct a Nether Portal and enter it.
4. Spawn a few Wither Skeletons directly in the portal frame using a Skeleton spawn egg.
5. Go back to the Overworld (make sure it's day), break the Nether Portal, and fill it in with solid blocks.
6. Observe how the Wither Skeletons run for the shade and water like a normal Skeleton, despite being fire proof.