We have a Samsung Fridge/Freezer, Model SRF527DSIST.

Of course it is worth fixing! This leak is cause by a defrost drain that is blocked with ice and sludge. I really can't tell you how to remove that rear panel unless you provide a model number. This problem is worse with the Samsung dual evaporators as the evaporator inside the fresh food compartment is usually the one that causes problems on those models. There are a few GE dual evaporator refrigerators also that are really a Sumsung with the GE brand name. Here is a link that may help but you need to pay close attention to the videos and focus especially on your Brand
Leaking Refrigerators

APPLIANCE 911

The drain line in the bottom of the freezer is frozen over. Remove the back cover boil some water and slowly pour it down the drain to clear it.

HI.TERRY.freezer has to work at its optimum.for the ice maker to work. i would try to defrost the freezer completely first and try.good luck.Ali

most likely, to clear you will need a bowl of hot water, an empty bowl, and a turkey baister. remove everything from freezer, and then remove the shelf. if you have an IceMaker remove it too. then remove the back panel from freezer, should be only 2 or 4 screws 1/4", then it will pull forward. you will see the ice in the evap drain. remove as much ice as you can, careful of the coil. the pan is flexible but try not to deform badly. then fill one bowl with hot water, hotter is better, using the turkey baister put hot water down the drain hole, let it set a few seconds and **** back into the baister and discard in to empty bowl... repeat until drain runs free. reassemble and restart fridge.

Ok one of two problems. Either you have an ice block or you have a plugged drain. If you have a couple of dif choices. If you have a back up fridge than fill it with the contents of the broken one. Unplug leave doors slightly open for about 48hrs. Have towels for the water from the ice. Usually 2 or 3 bath towels. Plug back in and if the problem happens again within a week than your bi-metal ( defrest thermostat) is bad. To replace you have to remove the back panel in freezer and and on the condenser coils near top you will see a little round silver part.
Option 2- If no backup fridge or you have time. Have a hair dryer, 3 bath towels, a 1/4 inch nut driver (may be phillips) for screws. Unplug fridge and open freezer. Remove contents and place in ice chest with ice.remove screws from back wall pull panel forward. If you have an ice maker ther are two screws on the top where the ice fills at and one at the bottom. Also disconnect the quick connect for the ice maker. Remove back panel. You will see one of two things either all your coils are iced up (frost on all coils is normal) or two where it drains on silver plater has ice blocking drain hole. If ice is blocking drain remove and pour hot hot water down drain until it flows into drain pan in the back of fridge by compressor. If the coils are all iced up have towels ready. Start by putting a towel where it would normally drain where the towel is soaking up the water. Turn hair dryer on and melt ALL thee ice. some ice will be in the middle of coils and in back where you Cant see. Keep the hair dryer moving sitting in one place too long can damage wire and the walls of freezer. Melt all ice until no more water is falling from condenser coils. Than you will have to replace the bi metal. Put everything back in and plug in wait about 2 hrs before putting contents back in freezer. Just to let you know the the fridge will NOT cool down until freezer gets down to temp. Than the air will start cycling into fridge. If you have anymore question please feel free to comment me back for further assistance.

just needs to be defrosted ice is blocking the vent for the bottom defrost it and should be good

Check the ice maker. sometimes they get cracked a will leak water into the freezer compartment. Also check the ice maker fill tube for leaks or someone could have spilled something. Although this is tipical of a clogged drain. What happens is when the fridge go into derfost, it will melt all the frost that is on the evaporator, turning it into water. The water drains down to a trough under the evaporator and down a drain hole in the trough ( this trough is behind the evaporator cover ) Removing the melted frost from the freezer. If that drain is clogged, the water cannot leave the freezer. Then when the fridge starts back up ,it will freez the water that was not drained. After repeated defrosting the water will fill this trough and run off into the bottom of the freezer to be frozzen when the fridge starts to cool again.

remove freezer back panel and you will see a tray at the bottom with a drain hole in the middle and it is this which is blocked. if blocked with ice, clear with some hot water and make sure drain is free and water flows away

Sounds like a blocked defrost drain. By "American" I presume you mean side-by-side.
I had a similar problem with a freezer-on-top style Samsung. The solution to that was to defrost the freezer, remove the false backing plate in the freezer (required removal of the ice cube tray. the panel just pops out with a bit of pulling). The drain hole beneath the freezer coils was blocked with ice. This drain passes down into the fridge and then out the back of the fridge into the evaporation pan next to the motor. There is a collector pan under the freezer coils, this and the drain hole were filled with ice. When the freezer goes into its self-defrost cycle the water collects here and then overflows into the fridge.
I removed the ice with hot water/vinegar mixture (so it doesn't re-freeze immediately) and simultaneosuly used a bit of chiselling with a screwdriver to clear the drain plug. I did this from inside the fridge working up the drain hole into the freezer. The whole job took about an hour.

you have a froen drain thats why it is allways getting ice on the floor. you need to remove as much as you can then remove the back of the freezer so you can clear the drain pan and clear the drain. its not hard to do just you will have a lot of water on the bottom and your floor maybe. once you remove the ice from the pan have some very hot water and pour it in the pan utill the drain is free and the water go's down into the drip pan. shut the unit off untill tour done and be carefull around the coils. once its clear put the back on and plug the fridge back in. you will now have no more ice build up. make sure there is no food back there that can block the drain either. its a god time to clean the freezer out