When you say it “freezes,” what do you mean specifically?
Only a few things can run when the Internet is down, and you will not be able to use your mobile app.
The only things that can continue to run are those that are eligible to run locally. That’s basically the official smart lighting smart app and some parts of smart home monitor.
But they will only actually run locally (operate even when the Internet is disconnected) if all of the devices that they use are also eligible to run locally.
Just as an example, hue lights are not eligible to run locally. So if you have a smart lighting automation which includes a Hue bulb, it will not be able to run when the Internet is not available.
Also, if you use any custom device handlers, they will not run locally.
I would start by looking to see what you have eligible to run locally. You can use the links from the community created wiki to check: