We've had this Woods frost free upright freezer for about 10 years and it works fine. But for some time (maybe since we moved it around) the drain water line freezes where it goes through the bottom of the rear wall into the overflow line. So the condensation water freezes and builds up in the bottom of the freezer. Should there be some insulation, or something else down there to stop this?

NO, But you can use a copper wire over the evaporator coils and place a straight part down into the hole to keep it from freezing. Although not recommended by WC Wood Co. Whirlpool says itcan be done and we have done several of the like that over the years.
If that doesn't sound appealing, get a defrost drain heater, part # SH250.
Nat

With the copper wire you make a "shepards hook' place the hook over a coil on the evaporator and the long straight part goes down and thru the drain hole a little bit to keep it from freezing.
Nat

According to the Supco catalog "Tech Tip" - The SH250 Universal Drain Heater is designed for “series wiring connection” only. However, Supco Engineering told me this is incorrect. The SH250 is designed for "parallel wiring connection".