There currently is one option to travel by night train from Ötztal (Austria) to Cologne (Germany), taking approximately 11 hours: Namely the UEX 1300 operated by UEX.
UEX (Urlaubs-Express) operates seasonal night trains, including car-carrying trains (Autoreisezüge), from Germany to Austria and back.
You can choose a seat, a couchette berth, a whole couchette compartment, a private sleeper compartment or connected sleeper cabins.
You can bring your car, but only between the car terminals, and you book the vehicle along with your ticket.
Skis travel free in the ski compartment. A bistro on board sells drinks and snacks.
There is a reduced fare for children who have their own seat or bed.