Yes, the liar have some hats. There are two ways how to conclude this:
1. If they don't have any hats, then any sentence about them would be truth.
2. The negation of the sentence, which must be truth, is "not all my hats are green". For this to be true, there must be some hats that are not green, so there must be some hats in general.
1. If they don't have any hats, then any sentence about them would be truth.
2. The negation of the sentence, which must be truth, is "not all my hats are green". For this to be true, there must be some hats that are not green, so there must be some hats in general.