the temperatures of perishable foods should be kept below the maximum safe temperature of high risk foods, like milk, meat, and eggs (below 40*)… keep these in the RV fridge… keep non-perishable only in the dorm fridge if the power will be off for more than 4 hours… longer than that it will cool back down quickly when turned back on if everything was already cooled…
although mini fridges are not power gobbling monsters and use I believe an average of only 145W, and many use less… between 70w and 120w even… you could power it with a portable 400w inverter hooked to the battery…
if I were going to do this I would spring for a 4 cu. Ft. for about the same money as a 2 or smaller cu. ft. model…