Only just seen your post, so this may be outdated now....
I always visit over Xmas. This year booked flight only, but because of it being peak period, decided to book a guesthouse for a few nights on arrival.
Although I started looking around online in January, I found that many of the ones with good reviews were already booked up for Xmas 2012. Eventually, I managed to book one in Benaulim, south Goa for Rs500 a night.
There will be accommodation available at that time, but you might end up trekking around a bit and perhaps having to accept something that isn't what you really want.
My suggestion would be to look around online for something for a couple of nights so you have assurance of somewhere to stay on arrival.
Yes, i am agree with you..As it is the busiest time period in the Goa, you have to look for accommodation first..