Probably you already have your answer, but in case not...
As an RV'er, you likely already have all or most of the knowledge you need. Perhaps I can bring it all together regarding this question.
If all you wish to accomplish is to power is the RV fridge, even if it's a newer, larger 4 door fridge, and you're going to have it set to the coldest settings (thus maximum amp draw), you still won't be using anywhere near 50 amps. And if it's a smaller 2 door, it will use even fewer amps.
In order to know the precise answer, if 8/3 wire will be safe to use at 50 feet, I suggest you need to:
1) check the max amp draw of your fridge, and anything else you might want to have on from time to time, "at the same time". This would include lights, possibly a dehumidifier or small heater (if you live in a cold area), microwave, etc. You decide, your rig.
2) Add all the maximum amps numbers together to determine the total, max amp draw (peak load) you might occasionally require or want.
Amperage requirement information is printer on a nearly everything electrical (fridge, heater, light bulbs, etc) in one manner/location or the other, also possibly in the RV's manual, or at least, very likely on-line. Some items might not indicate "amps", but may instead indicate watts. That's just as useful, since you can use Ohm's law to quickly calculate amps if you know watts and volts.
3) Perform a web search for an on-line "voltage loss calculator" (or phone/computer App if you prefer). They are abundant. Some offer/require many variables for which you may not know the information, and others quite basic (better), easier to use for a non-professional, asking a few basic questions.
Look at several before choosing which calculator suits your knowledge/information/needs best and then bookmark it!
Generally then, you might then approach the answer to you question from two different ways (possible more):
1st) You might decide you want to know the maximum amps that your wire itself can safely carry over it's length and compare this number to you determined Max amps (load) required. (You will need: wire type and diameter, voltage at source, distance)
Or,
2) You might decide you want to know the size of the wire needed to support the expected total amps required and distance. (You will need: voltage at source, distance, desired amps, type of wire)
In all you'll need be working with some or a combination of:
Desired total amps (load)
Distance from electrical source (breaker box or receptacle)
Volts at electrical source
Wire size
Wire type (copper or Aluminum)
and possibly the Wire's insulation type, of any.
For a more detailed analysis, you might also consider the wire's type of insulation, if it will be used overhead, laying on the ground or underground and if there will be any conduit.
If you won't need to run all those items at the same time, choose the group of items that you would likely use "at one time" and base you calculations from that number. Fewer items, less amperage draw, smaller wire.
Also, just like going into a park and finding there's no 50 amp service, upon which you'd put a 50a/30a plug adapter on your shore power connection which results in having only one hot available, probably 30 amps, possibly 20 or even down to 15 amps.
In those times you avoid running two air conditioners, or maybe avoid running one air conditioner while the microwave is running. You adapt. This is really no different.
If your power source is quite good, no brown outs, strong steady voltage, you may be able to run a wire sufficient for the entire 50amp draw. Maybe the wire you have will suffice.
You might find buying 2, voltage meters (everywhere on-line) that are designed to plug directly into a standard 15 amp receptacle. The meters will have a small LED screen that displays the voltage and is always "on". Cheap.
Other units might offer voltage and amp draw.
Since your 50amp service is designed with two hots, put one of those meters in a receptacle on "hot 1" and the other in a receptacle on "hot 2". Now you have real time, immediate at-a-glance ability to "know" what your RV is actually working with, and in some cases, you might feel the need to take some action to prevent low (or high) voltage issues. (Reduce load, change sites, change parks, use generator).
I've given these little voltage meters out to dozens of RV'ers (in Mexico). The poorer the quality of electricity in the park, the greater the value of such meters and seeing real time what you have.
With the voltage loss calculator, you will "fill in the blanks" - input your data and get solid answers.
If you're never going to turn on the air conditioner (at this location), heaters, microwave or any other motor or high amperage draw devices, you might easily use a 50amp/30amp or even a 50a/15a adapter. Your motor home will "know" and adapt automatically to having just the one hot wire. Possible you have a voltage monitor which will protect your system by automatically shutting down from any of several unwanted issues, low/high voltage, reverse ground/neutral, etc. (Electrical Management System)
If your wire is only capable of much smaller amps at the length, you might be able to use just a 15 amp receptacle and appropriate adapters.
Risk of damage is higher with electric motors than many common electronics. A laptop computer has it's own voltage regulator (the brick on the power cord), many LED lights hardly care, and so on. Air conditioner, refrigerator and pumps are more sensitive, as some medical equipment.
And yes, it would be advised to have a separate breaker at the panel, but you already have breakers in the RV, probably a master plus individual breakers for various circuits. Two safety's are better than one.
Good luck!
