Austrian rail operator ÖBB has confirmed that their NightJet service from Amsterdam to the Austrian Alps will continue to operate this winter. 
Departures from Amsterdam are every evening at 19.30, stopping at Cologne and connecting to Vienna, and via Munich to to Innsbruck.  British travellers could choose to take the Eurostar to Amsterdam or go to Brussels and then change onto an ICE service to Cologne, picking up the NightJet there.
Anyone who joined Iain for the train travel sessions at the Birmingham and London Ski Show this year will know about the options for travelling to Austria on the NightJet.
Seats can be booked on the ÖBB Nightjet in the seating carriage, couchette carriage with 4-person compartments, or in the sleeper carriage.
For maximum privacy, the compartments in the three comfort categories can also be booked as a separate private compartment. This enables you to travel with just your family or friends, without having to share it with other passengers who are not in your group.

Connect via Eurostar to Amsterdam

You can connect from London via a direct Eurostar at 11.04. That gives you lots of time to connect in Amsterdam, with three hours to explore the Dutch city before joining the night train to Austria. On arrival you can change at Worgl to access resorts in the Tirol before the train finally arrives at Innsbruck.
Alternatively you could travel to Brussels and catch a connecting train to Cologne, before boarding there.
Another option is to travel to Paris or Brussels and catch the NightJet from there to Salzburg.
Note that apart from the Amsterdam to Innsbruck service, these trains don’t operate every day.
You can check the timetable and book tickets here.
According to SnowCarbon, some of the resorts that you can access are detailed below:
From Kufstein
25 minutes by bus or taxi to SollFrom Jenbach
20 minutes by bus or taxi to Alpbach

From Wörgl
18 minutes by train to Westendorf
25 minutes by train to Kirchberg
25 minutes by train to Kitzbühel

From Innsbruck
1 hour 8 minutes to St AntonFrom Salzburg
1 hour 29 mins to Bad Gastein
1 hour 16 mins to Bad Hofgastein
1 hour 16 mins to Schladming