I'll be out of grid for some days and I'm planning to have a small electrical fridge with me. It's a 12V 4A small fridge with a cigar lighter plug, but I won't have a car with me, so I think I could connect it to a 12V car battery? My questions are, does my plan make any sense? Also what do I need to know so I can figure out how long the fridge can run before the battery runs out?
It does make sense. Those 12V car fridges are usually not very effective though, enough to chill a few beers but will not freeze raw meat. How long it will work depends on the battery capacity and enviroment. For example if you have a regular lead-acid car battery with 75Ah capacity then it should be enough for roughly 75Ah/4A=18 hours of operation but with good insulation and well balanced thermoregulator it will be longer as it probably will not work all the time but will chill to some set temperature and then it will go off until it inner temperature rises above a set limit, so it is very hard to tell how long it will work in your case. NB. transporting lead-acid batteries is risky you need to make sure that you dont spill acid from it.