Lot's of senior members here with experience, which is great.
1. water lines - run antifreeze 'till pink comes out
2. shower hand wands inside and out - run them until pink, or just take them off and store in bathtub. be sure the outside shower faucet runs pink too.
3. drain traps - add some antifreeze in each sink, shower drain and toilet. a cup or two should be all you need.
4. waterheater - drain and bypass. cycle the inlet (cold water) valve on the bypass set up to get some pink in that section of line, don't fill the water heater. This trick won't work with the hot water line as there is usually a check valve.
5. black water tank - dump and flush as best as possible. any residual water will evaporate leaving the solids to further solidify, therefore flush well. no need for anti-freeze.
6. fresh water and grey water tanks - dump/drain and leave them. Again, no need for anti-freeze.
7. battery - fully charge prior to removal, remove and store where it wont freeze and don't store on concrete. Keep cell caps on. Don't leave it on a trickle charge all winter as the water may evaporate. Every two months or so, put it on a charger for a day. Prior to camping season, charge it again before you reinstall it on your trailer.
Errors on my part over the years:
- forgot to winterize the outside shower. hose burst the next year and flooded the floor.
- left the batteries on the trailer. CO monitor drained and dried the batteries.
Where I live near Puget Sound, I no longer use anti-freeze, as it doesn't get cold enough, long enough. I just blow all my lines with air. I set my compressor to 50psi, and use an adapter for the city water connection.