Nah, it was 38 class between Central and Goulburn and 32+32 class between Goulburn and Cooma. All locomotives fitted for steam heat. I cannot help much with the consist but the sitting cars on the one trip I did were MCEs and FS and the sleepers were TAMs, all fitted for steam heat
That's odd...when I was a child on the train in the late 60s/early 70s, the only heating was by the water-filled canisters, and they ran out of heat really quickly! I don't recall the TAMs being heated as it was freezing all night 
[EDIT]
And it was only diesel...
Neil, While tabled for a 38cl, it could also be a 36cl up front as the load was very much inside that for a pig. Problem was how many of those engines that had steam heating fitted were still in service? The temporary storing of the pigs meant they were not available, so careful rostering of 38's for the service was needed.
At the time only 4 32's were still available for the train with steam heating equipment, 2 based at Goulburn, one on loan to Temora 3326, with the other 3 3214, 16 and 82, with two generally kept at Goulburn. There was a period when one of the GLB engines was out of service and arrangements put in place that a non steam heater engine was to lead through to Cooma with the steam heated one on the train, the hope was that the single steam heated 32 would not fail, but they were rigorously checked over by the fitters at GLBN.
When the steam heating was removed, the carriages used on the mail as well as the ski service were fitted with electric heating which was basically useless, owing to the heat being supplied through a generator supply and jumper coupling arrangement on GLBN based 48cl and several Mk 1 44cl, the later working between Sydney - Glbn & Return. The problem with this arrangement was that to get the heaters working at the correct rating meant the diesels had to work in #4 T/N, something basically impossible for the overall journey.
The main part of the Short South was all uphill on the down, meaning the 44cl had to work in 8t/n for the vast amount of time, when going down grades or flats, the generator field was turned off so to just have the prime mover running at the higher revs to supply the power or use dynamic brake if working, that worked pretty well on the up as much of the up train could be well controlled by using dynamic brake. Catch was that often one of the few 44's that had the jumper arrangement may not be available, so the 2x48's took the train through to Sydney.
On the Cooma section, again the undulating and grading of the line did not provide the most ideal conditions as often just as the carriages were warming up a bit, there was a need to actually power up the train engines, baring in mind no dyno's on 48cl meant a constant running with the PM reving almost all the way.
I understand that as a concession, the foot warmers were also included in the trains when the steam heating was removed after the first few trips when the deficiencies with the electrical heating setup came to light.
From memory, the mail and ski express were generally a random set that had carriages fitted with steam heating and then with the electrical set up. TAM's were the primary sleepers and any of the 72'6 cars, or FS/BS were used.
There was one season in the 60's when an additional train was also run, it had no sleeping cars, but one carriage was stripped of seating with a band playing all the way. Sitting only cars were on it, however it only lasted a short time owing to getting engines available along with alcohol problems.
Finally, one Van was supplied for both ordinary luggage and for the extra's that skiers took with them such as ski's and the like, making 2 vans as required. IIRC, the service was also a booked seat train as well one of the first older type trains to go that way.