There are a number of issues here, and its not as simple as being the amount of snow on the tracks:
1) The staff have to get to the depot or siding to start the train and bring it into service - they need to get to work long before most of us wake up so travelling in the night may have been difficult...and they need to get home again after getting the train back to a depot;
2) The train engine or air system may have frozen if its been parked outside all night;
3) The platforms have to be cleaned so the platforms are not slippery when people get on or off the train - in the old days a stationmaster did this - these days it is a man in a van if he can get through the weather!;
4) Similarly, Network Rail need signallers to turn up for work;
5) The track and points need to be cleaned of snow and ice so they're not frozen and signalling works okay.
Yes - I agree with you / with that list.
I cannot speak for any other lines, but I can give you some answers with regard to the TransWilts:
1. The trains used on this line were both in service and staffed. The unit on the 05:19 from Gloucester (that's the time of the first of the two trains scheduled southbound on the line!) did run to Swindon, where it waited to pick up the northbound diagram. The unit that would have been used from the northbound 07:02 from Westbury picked up the southbound service at 06:59 to Southampton
2. Same answer as (1)
3. It may be that the platform at Melksham had not been cleared; I wasn't there personally, but I was certainly out and about in Melksham and the snow was even and not deep. I'm pretty certain that a man in a van could have got through
4. The line is signalled from boxes which were all open.
5. The closed section was a length of single track, with other services running over the points at both ends. The signalling is colour light - even in Melksham, they've moved forward beyond Abbotts Ripton
Whilst I agree with you on that list, I don't see that any of them actually should have applied in the case of this line / these services, and I remain somewhat leaning towards sharing the view:
The SNOW has not stopped the trains running !
What has stopped them is: lack of staff, fear of litigation, and finally - the "easier not-to-try" attitude, AND of course, total unwillingness to do anything that might cause additional expense to the Company - overtime, diesel, electricity, foul weather clothing, etc, etc