Just because other airlines were able to continue to operate means nothing unless they were operating the same aeroplanes, and even then there are differences. Your airline might operate aeroplanes that can't land in the thick fog that another airlines can, even with the same aeroplane type different companies have different limits on all sorts of things. In your example you quote "heavy snow", some operators might restrict operations on runways with different slippery conditions dependent on their risk assessment.
All these excuses but the fact is these are operational, not weather issues.
The carrier may have decided not to fit the Cat 3 kit on their aircraft which others do, or not to train/maintain the currency of crews in its usage. That's an operational and penny-pinching decision, not a weather issue.
I have been delayed in the UK "due to the snow" on a carrier, where the same carrier has operated with me, on the same type, quite happily in the snow in Finland and Russia (where if you didn't there would be little winter service).
I've also been cancelled "because as you can see it's snowing" where in practice their handling agent had run out of de-icing fluid ...