After reading multiple posts on various web sites, this is what I think makes the most sense:
Begin adding stabilizer before your last one or two outings. Do this while the fuel is very fresh. This insures that it stays as fresh as possible and also gets into the fuel line and carburetur.
After your last outing, if you have a portable tank, fill it up (unmixed) and add fuel stabilizer. This will protect the tank from corrosion. But then dump the fuel into your car in the spring and start fresh with your boat. If the tank is built in, use up (or drain) fuel as much as possible before storage. Fill with fresh fuel before your first outing in the spring.
In both cases you want to eliminate or dilute the stored fuel as much as possible before running it through your motor because the alcohol in the gas absorbs moisture over time. Also, I am not convinced that stabilizers do a perfect job of preventing the formation of all the gummy products that are found in old gas.