A 50 watt panel will generate up to about 25 AH/day. That maximum is only possible on a clear day with no obstructions and in mid Summer with the sun directly overhead on the panel.
I have a small (4 cuft), efficient Nova Kool compressor refrigerator. It pulls about 2.3 amps when running. At roughly 70 degrees it runs a minimum of about 10 hours a day for 23 AH. If the ambient temps are higher, or the refrigerator is opened numerous times, or if you add any items that need to be cooled down, the compressor is going to run much longer and can easily eat up 40 or more AH/day.
I would recommend at least 200-300 watts of solar in order to generate sufficient power for the refrigerator, lights, water pump, and minimal use of a furnace. The rule of thumb also requires roughly 200-300 AHs of battery bank. I have 270 watts and still need to use a generator for cloudy days, when not parked in direct sun, and for Fall-Spring use when the sun is lower in the sky and less intense.