If your freezer is on your local wifi and your computer is also on the local wifi you should be able to see all the packets it is transmitting over the wifi with Wireshark on your computer. If either your computer or freezer has a hard connection then you'll need a little more trickery as switches/home routers minimise network congestion by directing traffic to specific MAC addresses as required.

Assuming you are all wifi, basically you load Wireshark (is free software, easily downloaded) and tell it to capture all packets from your wifi adaptor (there should be a handy option on the initial screen when you load the application). Once you start capturing you'll be capturing everything on your wifi so it pays to be quick with what you want to achieve to minimise the data.

So, once you start capturing you open your fridge door a few times, leave it open till it beeps, maybe do that twice, then stop capturing. Following that you will just need to filter the capture by all packets from your fridges network IP or MAC (you should be able to find these from your home router). Once you have all the packets you should be able to click on them and expand all the details to see what data they are sending and where it's being sent to. You should also see all the packets coming back from the vendor.