I've found that these are the most common causes of wet carpeting in front of the refrigerator:
Plugged Drain Tube
This is the most likely. It's a white tube you can see from the outside. The end rests in a black metal cup. When the tube is plugged, the tube fills with water. Then the drain tray under the cooling fins inside the refrigerator fills, freezes, and overflows — check it for water and ice. It's normal for it to be wet, but there shouldn't be any significant buildup of ice or water. You can also run a pipe cleaner through the drain at the low end of the tray (usually on the left), though the real problem is usually outside at the end of the white drain tube.
The tube has a very small black tip that clogs easily. You can clear it with a pipe cleaner (I keep one in the outside compartment and clear it every week or two). Run the pipe cleaner horizontally though the "eye" at the end of the tube, and also vertically up into the tube (water will squirt all over your shirt if you don't aim it away from you).
Don't be tempted to remove the black tip from the tube. That will allow too much warm air up the tube into the refrigerator.
Overflowing Drain Cup
Another possiblility is that the black cup the drain tube ends in has overflowed. The water in it is supposed to evaporate faster than it collects, but in humid weather when you're opening the refrigerator door a lot, it may not.
Some people run the tube out through the grill and let it drip outside. I think not sitting in the warm water helps keep it from plugging up. If the cup overflows, the water can run under the refrigerator to the carpet.
Leaking Container in the Fridge
If you lay bottled water or some other bottled liquid sideways at the front of the refrigerator and the cap is loose, your carpet will get wet.
Leak in the Icemaker Connections
These are on the outside. You can get to them through the outside access panel. This is easy to diagnose — just open the outside hatch and see if any of the water connections is wet on the bottom. The most likely is the one that looks like a hose connection. If it leaks and your floor slants toward the coach (mine does) the water will run under the refrigerator and wet the carpet.
Water off the Slide
If it's been raining and the refrigerator is in your slide, water can come off the back of the slide and wet the carpet there. My slide often has a little lake on top of it so if you bring it in wet, acceleration wets the carpet by the fridge, braking wets the carpet behind the the driver's seat. Even with the slide out, the right combination of wind and rain can get the carpet wet.
Water off the Roof
This is fairly rare, but there can be a hole in the rain gutter where the slide awning is attached. Water from the air conditioner can run down the edge of the slide and wet the carpet.
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— Bob Ray