I too question the #16 AWG. Will it work? Probably. Is it a good idea? Probably not. 16 gauge as a resistance of 4.016 ohms per 1000 ft., more than 4X that of 10 gauge. At 30 Amps the voltage drop would be 15. 6 volts, which is getting pretty near brown-out territory especially if you have poor shore power at the campground.
The other factor is current. Are you always drawing 30 Amps. Of course not, but the AC unit can draw between 12 and 16 A, a refrigerator
will draw between 5 and 8 A, a microwave
between 8 and 13 A and a coffee maker between 5 and 8 A (see RV Converters and Amp Draw - RV Information (RV Maintenance)
). They all add up and I haven't considered lighting
(hopefully, we're converting to LED's).
Brownout primarily affects motors (AC compressors and fans, refrigerator
compressors, pumps, etc.) but can also affects electronics (TV's, computers, etc.). If the voltage gets too low, the electronics simply stops working or does something unpredictable, but usually does not result in damage. Motors, however, are a different story. The worst case scenario for a motor is what is called the "locked rotor" where full current is provided to the motor but is does not or cannot turn. Unless specifically designed for this, the motor will burn up in a very short time. Increasing the load on the motor can slow it or even stop it (locked rotor), so can reducing the voltage to the motor. When the motor runs, it actually generates voltage that counteracts the incoming voltage and reduces the current through the motor. This is called Back EMF (Electro-Motive Force). When the voltage is reduced, the motor slows, but the load does not change causing current through the motor to increase, if this continues, permanent damage will occur. I hope this is not too long and technically detailed, but thought it would help with everyone's understanding.
Bottom line. Heavy duty cords are not that expensive. 100', 12 AWG cords are available at you local hardware store and would likely be adequate on all but the largest RV's.