Save the pattern while it is fresh
Write down when cooling started, when airflow weakened, the thermostat setting, and the room temperature. Does air fade at every supply vent or only one? Does the indoor fan still sound like it is running? Photograph ice or water only where it is visible without removing equipment covers. Do not restart the AC just to recreate the problem.
Check the owner-accessible filter using the equipment's instructions. Record its size, type, and condition. Look for furniture covering normal supply or return grilles. Those observations help, but a dirty filter does not prove it is the only fault. Leave the required filter installed and avoid changing blower settings.
Ask for a diagnosis after thawing
A frozen coil can hide the original problem. The service provider needs to know about the hours-long delay and may need to observe a complete cooling cycle after the ice has melted.
We would ask for measured airflow and refrigerant-system findings, the indoor fan's operation as it warms up, and any control or drain findings relevant to the symptoms. Ask what evidence supports the proposed repair and what ruled out the other likely causes. The useful result is a written finding, rather than “it needed some refrigerant.”
Once the repair is complete, ask how the technician verified that airflow stays steady through a meaningful run. A few cool minutes at startup would not address your original complaint.
Keep cooling off while ice or serious airflow loss remains unresolved. If indoor conditions become too hot, use another cooled space while arranging service. Send the timing notes, filter information, and safe photos with the appointment request so the visit starts with the failure pattern.