You can look on E-Bay and look up Kill-a-watt, it is a $30 meter that can monitor the input voltage. Many campgrounds with only 30 amp service suffer from low voltage, and that is probably the condition that you have.
Voltage is the pressure and Amperage is the flow. Your site did not have enough voltage (think pressure). Amperage is what will flow into the electric cord as items inside use them. So it had the ability to flow more power, just your ice maker does not like 105 volt power input.
You can buy a Hughes Autoformer, and plug that into the low voltage campground power. When between 115 and 120 volts, it will give a 3 volt boost. Once below 114 volts, then it will boost by about 12 volts. This will make both the compressor in the A/C and your ice maker very happy!
My suggestion: Make more ice before leaving, or buy ice. It is normally pretty cheap to buy the ice, and will not give off heat into the location of the freezer or ice maker. . .
Fred.