Just like an AC, a heat pump *can* ice up. Also, a heat pump *will* stop working at some magic temperature in the vicinity of 40 degrees. The closer it gets to that magic temperature, the colder the air out of the heat pump will be.
Next up, if you are shooting for 80 degrees in the trailer and it's 110 out, the system will struggle a bit. It will handle a 30 degree delta, but only sort of. The same thing will happen if it's 50 out and you are trying for 80. The system is going to struggle.