There are plenty of articles on the Internet on travelling with dogs. This is just one:
https://www.travelnuity.com/dogs-on-trains-in-europe/ 

As far as I know there are no differences when you use a pass to standard ticket passengers, but be careful to pay any supplements the operator sets - these are not included in your pass.

Note only guide dogs are permitted on Eurostar.

 

If you plan to travel to Sweden you must make any needed seat reservation in the compartment allowing animals.