What I do for Winterizing.
1. I put Sta-bil in the gas tank and fill it up. It is best to have the tank full to prevent any condensation or rust from developing. The Sta-bil keeps the gas from going bad over the Winter.
2. I try to change the oil relatively late in the riding season. The fresher oil, the better, because oil tends to build up acids as you put miles on it. I'm not sure if the synthetics are any more or less prone to that than conventional oil - I do use synthetics.
3. I keep the battery on a smart charger. I currently use Battery Tender Jrs, and they work fine. You can get them for about $20 at Arizona Motorsports. I do not remove the battery from the bike since I have a garage with convenient power outlets.
That's about it. I've been doing this for a number of years with good results. One advantage is that the motorcycle or scooter is ready to ride if we catch a few mild days during the Winter. I do normally get a ride or two in. I have electrically heated riding gear, so it is road conditions (snow, ice, sand and salt) that keep my bikes off the road more than the cold. At worst, the bikes sit for 3 months.