Thanks for the replies!
Peariso: I took your advice and removed the skirt. Oh my god! it made so much of a difference. I like it so much better now. It has small wooden legs that it sits on and they just make it look so much cleaner and nicer looking. Honestly, I was so shocked at what a simple solution that was! Turns out the skirt was only held on by a couple staples and some loose stitching, so it came off really clean and quickly. I was thinking I might recover the front section with the fabric from the skirt, but like you said theres not quite enough, so I'm considering maybe attatching it as sort of a panel on the bottom, right on top of the holes.
Like in this picture, but it would end where the arms connect to the chair (where you can see the seams) and the bottom would be much cleaner looking and not have all those loose threads. Also, obviously it would be much more flush with the chair, since I won't just be holding it on there.
Would that look really weird?
This is how it looks without the skirt. Do you think I'd be better off just patching the holes somehow, or stitching them up?
Thanks again for all the great suggestions. I would just take it somewhere to have fixed like hercuteness said, but its not quite in the budget.
And I dont really want to completely reupholster it because I love the fabric and the antique look of it.