The worst thing you can do is to leave untreated, ethanol garbage gas in your tractor for the winter. The advice given by some here to do so is just asking for problems. The fuel will create condensation (water), turn toxic and the ethanol in it will eat away at rubber & carburetor parts.
First off, use the correct amount of Sea Foam (1 T. per gallon) ALL CUTTING SEASON to neutralize the ethanol. Then, when you've done your last cut for the season, figure out (overestimate rather than underestimate) how many gallons it will take to fill the gas tank to the top, & add 1 T. per gallon. It doesn't have to be exact, it just shouldn't be double or more the correct amount. Then start your mower up, run it for 10 minutes, engagement lever off, just to circulate the Seafoam so it gets into the carburetor.
From everyone I talk to and reading of posts, I don't think it is necessary to have the gas tank full, but it should at least be 2/3 full.