Assuming your battery is in good shape, if you have a generator you will be fine. Your fridge needs the power to operate. If your battery is older or has been too discharged in the past, maybe it's time for a new one.
We can go three days without running the generator, although it's rare for us to run the furnace more than an hour or so in the morning to warm things up, (and we're in a PUP, so it reaches ambient temperature with the outside pretty quickly). We run our generator in the evening when we return from hiking or biking and are taking showers. The water pump is a pretty good load plus Allison can then dry her hair afterward. You can run your generator from 7:30 to 10 am and from 4 to 8:30 pm. at Moraine Park CG.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)