Seat Ateca air conditioning mirror heating and frozen nozzles

Frozen spray nozzles and no AC sounds like a faulty vehicle temperature sensor. Have you checked the sensor's wiring and connector? A loose or corroded connection can cause weird issues. Sensor diagnostics with an OBD2 scanner might show a relevant error code. If you're getting a reading that's way off, it's likely the sensor itself or the wiring.

When you say 'OBD2 scanner', is that something I can just buy online? I've seen some cheap ones, but I'm not sure if they're any good. Where is the outside temperature sensor located on the Ateca? I had a quick look, but couldn't spot it.

An OBD2 scanner reads diagnostic trouble codes from your car's computer. A basic one will do for reading codes related to the outside temperature sensor. They're pretty cheap online. The sensor's location is usually behind the front bumper or near the side mirror. Since you're getting multiple issues, it's probable the sensor is faulty or has a wiring problem. Given the cost estimate you mentioned, it's worth getting it checked out at a workshop. They can pinpoint the issue and replace the sensor if needed.

I wanted to say the garage confirmed it was the outside temperature sensor. They replaced it, and now everything is working. AC is blasting cold air, and the mirror heating is toasty. The total cost was 95€, like you predicted. Thanks for your help.