Booking Accomodation in Torres del Paine

Hello,

Just had a quick question about booking accomodation whilst trekking the 'W' circuit. My partner and I are planning to get to Torres del Paine in early March but don't have a set date, thus making it hard to book accomodation at the various campsites along the circuit. Do you think we could get away with not pre-booking accomodation in early March? I've heard it is essential in January/February, I was just wondering whether by March if it easier to get accomodation without having to pre-book.

Thanks a bunch.
Luke