Some of the hotels would probably like you to book ahead, but, no, in October, you'll have plenty of choices. A few places could conceivably be booked on a given day, so if you have a place you just must stay at, I'd book ahead; otherwise, no, just show up and check around. Taxi drivers will try to take you to various places, most of which pay 20% or commission to them, but you'll probably get a better deal by stopping in and asking politely for the rate.
I personally like to know where I'm staying, but if you can stand the uncertainty, then go for it.
--Lan Sluder
Belize First Magazine
http://www.turq.com/belizefirst/