Unless there is one of those "unusual cold fronts" that come through, being along the coast should not be that cold. The trailer you're renting should have a furnace that runs on propane. If you've not towed or had any experience with a trailer, suggest you make a call to the place you're renting and ask for a time to get some instructions before you're actually ready to head out. You also need to know if it's 30 amp or 50 amp so you can be sure the campgrounds you'll be at have the right electric supply for your site....most likely it's 30 amp. You can use a small electric/ceramic heater and will probably be just fine. A couple of blankets or a heavy quilt should suffice along with socks at bedtime. Agree on the sweat pants for PJs. Some friends who camp in weather colder than we choose to, swear by wearing a knit cap to bed.
BTW, if you do use an electric heater, don't even think about turning on the coffee maker or using a hair dryer at the same time as you'll most likely pop the circuit. Heat generating appliances are a big draw, so turn the heater off for that time.
Have a great trip!