A leaky gasket will let more moisture into the fridge, which will then build up on the freezer plate via deposition. Deposition is the phase change between gas (vapor) and solid (ice). It will build up like snow on your freezer plate, taking up all the space and making it impossible to fit your frozen foods into the compartment. This picture was taken after I had poured some warm water on the ice in an attempt to remove it from the freezer plate.
Warm water works well, but it is very time consuming. A heat gun is another and quicker alternative. The slowest option is to leave the freezer off and simply waiting for it to melt off. Under no circumstances should you ever take an ice pick to the ice! One small puncture will destroy the freezer plate and drain your system of its refrigerant. If you damage it with an ice pick, the only solution to repair the system is to purchase a new freezer plate and recharge the system; which will set you back several hundred dollars!
Top loading fridges have weather stripping gaskets that get old and beat up over the years, loosing their seal and allowing moist air to enter the fridge. The best solution is to remove the old weather stripping and replace it with new weather stripping.
Removal is very simple, as weather stripping is attached with a weak adhesive. Simply roll up a corner and begin peeling it off. Once removed, I suggest a thorough cleaning of the lid and sides of the fridge as the weather stripping can make cleansing difficult.
Once everything is cleaned to a satisfactory level, begin laying down the new weather stripping. Set the weather stripping at one corner and unroll it as you adhere it to the edge. Pull it all the way to the other end and then cut it with scissors in place.
Once it is stuck down, peel the white backing paper off weather stripping. Always pull the backing paper off at a sharp angle to avoid lifting the weather stripping off the flange. If the weather stripping does lift up, simply re-position it and push it back down to adhere everything.
Once finished, check for any open corners where the weather strippings might have pulled back and opened up as these openings will leak in warm and moist air. If the corner is open, lift up the last few inches of the weather stripping and tack them back down in contact with the other leg of the seal; this will ensure that you end up with a tight seal which will keep out moisture and make your fridge run more efficiently!