This does not work insofar as they still need an Internet connection for the services addressed, of course. Alternatively, the following trick works:
Set up the Chromecast at home (or simply an existing WiFi), then set up a HotSpot (quasi access point) via the mobile phone during the holidays, which has the identical access data as the pre-configured HotSpot (i.e. identical SSID and password). The Chromecast then logs in automatically via the mobile phone. After that, the services mentioned, such as Zattoo, can be used without any problems. Sometimes it only takes a little longer for the mobile phone to find the Chromecast in the internal network.
The only thing to note is that the data will then of course run via the mobile phone subscription. This means that an unlimited connection would be highly recommended. Otherwise, there is a risk that you will have completely used up your data volume after watching half a film on Netflix.

Thank you very much for your detailed answer. Of course I know that I need a data connection for the services. The AppleTV has a peer-to-peer AirPlay function, I was hoping that Chromecast would also have one. As far as I know, your suggestion is not possible because the iPhone only releases the data connection, but does not create a network in the conventional sense! But I will certainly test your suggestion.