Smaller solar panels can help maintain the battery while the trailer is not in use, though to power the refrigerators control electronics, run LED lights at night, and charge the battery enough to power the furnace blower fan during cooler nights you will likely need 150 -200 watts worth of solar panels minimum if camping in the spring or fall with shorter days, if not you would still need to run a generator to keep your batteries charged while camping.

Here goes the math

Knowing the exact model of refrigerator and furnace you are using would help give a better estimate, though as a general rule an RV refrigerator will consume 5-8 watts of power for the control electronics, which would run 24 hours per day. Lets assume on the high side so 8 x 24 = 192 watt per day, lets round that to an even 200 to keep things simple. Lets assume you have a small Suburban brand NTQ series forced air furnace, which has an amp draw of about 3 amps while running, 3 x 12.8 = 38.4, rounding again gives us 40 watts per hour, assuming running only at night, 8 hours per night, for 30 minutes out of every hour. 40 x 8 x .5 = 160 watts per day. LED lights should be trivial in comparison, even assume you want it fairly brightly lit, a 60 watt equivalent LED light bulb draws about 9 watts per hour, let say 3 hours per night we are still just under 30 watts per day. This all brings us a grand total of about 400 watts per day you must replace into your battery.

For mid America average spring / fall lighting levels a fixed mount flat solar panel will generate 4 to 5 hours worth of peak output per day if exposed to open sky. Shading can reduce this considerably, battery charge losses account for 20-25% of the total solar output. So working with a single 150 watt solar panel with 4 hours of peak output per day we get 150x4 600 watts per day x .75 for battery charge losses, and we just about break even at 450 watts of available power added to the battery on an average day. Of course you may want to go larger in case of cloudy weather, wanting to recharge cell phones, run radio, etc.