Over the years I have found that when campground camping in cold weather it pays to be prepared for the worst! By the worst I mean a sudden cold front that blows in bringing the temp down to about 20 degrees ferinheight and the air mattress your sleeping on just allows the cold air to get you not only from the top but the bottom. Tents are mostly designed to breath so it's hard to trap enough heat in. A portable heater will just go up and out through your rain fly, and can be dangerous around flammable material. So what do you do?
Heated mattress pad! For two reasons. One the heat wants to rise, if the heat is coming from underneath you it will be trapped in your covers and keep them warm as well. And two the heat will keep your air mattress full of air. As it gets colder the air inside your mattress will shrink causing your bed to sag, very bad for your back.
Why not a heated blanket? A heated blanket is ment to go on top of you not underneath, what I have found is that this keeps you top half warm fine, but the air in your mattress will slowly cool down and your bottom will get colder with it.
A queen size heated mattress pad will run you about $30 and will fold down much smaller than a blanket for space. I always have ours with us, it is just a part of our equipment. We learned our lesson one day in late March in FL when the day time temp went from 75 degrees to a night time of 20 degrees. That was a miserable night!
Sometimes it the little things like a nice warm bed on a cold night that makes your trip just that much more relaxing. Enjoy!