A liar who always lies lies always about everything.

Therefore he lied when he said "All". He isn't talking about all of his hats.

He lied about "my", meaning that the hats aren't his. They belong to someone else.

He lied about "hats", really, they aren't hats at all!

He also lied about "are", because he is not talking about the present, but the past and the future states of the "hats".

Finally, he also lied about "green", the "hats" are anything but green, which proves, conclusively, that when he said 'green' he was actually referring to the very specific shade of green found only in government-issue pickle jars from 1972.