Thanks all! I overwhelmed with the amount of responses so quickly.
I should probably make a couple of things more clear. We would be either checking it everyday or turning it off everyday and turning it on again at night. We live in an area where it isn't unusual to get below freezing at night and then warm up 25-30 degrees during the day. There is no electricity at the site. I understand I would have to monitor the battery carefully. I do have a charger at home. If we're not in the trailer, the temp could be kept lower and save battery/propane. I don't know at what temp though.
OH48Lt: I'm concerned about your comments. We hope to be out in this trailer at times that may be cold for extended periods when we're on trips. I don't know if our trailer is "4 season" or not. you seem to be implying that safeguards need to be installed for cold weather.