As another translation for this nonsense sentence, "Will the cow going to wear a hat?" should be also correct.
Sorry. 'going to' was mistakenly added.
Will and going cannot be used together. You could say "Will the cow wear a hat?" however.
Yes. you're right. my mistake.
so will write and will wear are written exactly the same?
Yes, but keep in mind that 쓰다 is mostly used for wearing a hat. For clothes you have to use 입다.
Why 'will the caw wear a hat' is wrong.
Yes, yes she will.