Gameplay wise: If skeleton horses were to burn in sunlight, it would be almost impossible to keep them in survival. Yes, they spawn during thunderstorms, meaning they are protected by the rain, but most players find skeleton horses after the thunderstorm ends.

Lore wise: Since they spawn only from lightning, we could say that skeleton horses have some kind of heat immunity, similar to husks, while zombie horses are similar to regular zombies, meaning they aren't immune to sunlight.

But that's just my opinion, what do you think?