In every case that I can think of, LE DID search the home, or the last place there was a sighting.
I would be very surprised if they didn't do a quick cursory look in the trailer. You have 'probable cause' in the fact that you were called to do a wellness check. Someone has been reported missing, so you check where they are supposed to be.
Now they couldn't do thorough forensics, like with luminol, etc. Or look at the phones or laptops, or the GPS in the vehicle.
But they could look for a person, alive or dead, to rule out an accident or an illness.