YOu never know about near Christmas. School goes right up almost the last minute (well it certainly felt like it LOL!) and they only get two weeks off. A nursery attached to a school will still be running and will often need supply cover. I used to get bits and pieces of supply work covering teacher training, staff having to leave their class to organise the school Christmas play etc. So you never know. Sign up with an agency now online. I had a callback within an hour when I applied online when I was in Australia and thinking of going back. After 3 years in Australia unsuccessfully trying to get teaching work I was surprised at the amount of education based work there was here (if you don't want a perm job that is!) Teaching and education agencies are more proactive here. Having spent 6 years in the UK I couldn't believe that I had to do all my jobsearching myself in Australia!! The Australian agencies were rubbish!
If you do do supply work, don't feel you have to do the first job they give you. I used to get a phone call every morning. If I didn't feel like working that day I would ignore the phone. If I did, I knew they would try and sell me their least enticing job first. If I didn't want what they had to offer first, I would ask what else they had. They always had something else when pushed!
Good luck and hope it snows for your first winter here!