Accurately forecasting storms, rain or snow for the Blue Mountains and Central Tablelands in general takes skill and experience and can't be learned overnight. Still, with a bit of effort, almost anyone can develop a good basic, forecasting skill set, thanks to the information available on the internet. I can't think of better guides than the ones from Jimmy Deguara and Anthony Cornelius. Please read the 'Storm/Weather Forecasting' and 'Observation Techniques' links above if you really want to learn the nuts and bolts of storm and weather forecasting. It will take a good amount of time and some real effort but its also very rewarding. Special thanks to Anthony and Jimmy for these excellent guides. This approach is what most skilled forecasters (professional and amateur alike) use for day to day forecasting.
Its understandable that not everyone has the time or inclination to become a forecaster, so below are a few basic forecast reminders.
Its important to remember that a forecast for the Central Tablelands is a general forecast for the whole region, not just the township of Blackheath or any other individual town. The Central Tablelands forecast district is roughly 300 kilometres long and 200 kilometres wide. Starting near Katoomba in the east it stretches past Orange in the west, then past Mudgee in the north and towards Taralga in the south. Its a very large area to forecast in. So, when the forecast is for scattered storms or the chance of a storm or even possible snow, it means just that. It doesn't mean that the little town of Blackheath (or any other town) will definitely get storms or snow.
Storms are small, isolated cells that form around areas of atmospheric instability, so whilst Blackheath will get its share of storms, so does everywhere else. Storms can be a hit and miss affair in this context. The same can be said about snow. It depends on moisture availability and where the coldest air positions itself in the upper levels along with the appropriate surface trigger. This will usually determine which towns get the best snow in the Central Tablelands. Of course, western areas of the Central Tablelands (Oberon, Shooters Hill, Black Springs etc) also benefit from topographical uplift from the lower ground immediately to the west, so even fairly dry cold outbreaks can produce light to moderate snow in these spots as the cold air is lifted over higher ground.
So to recap, a general Central Tablelands forecast is for the whole region not individual towns. Read forecasts carefully. As a very general winter rule, significant weather from the west and south-west usually produces more rain/snow for the western areas around Oberon etc and significant weather from the south around to the east, typically produces more rain and sometimes even snow for the eastern areas like Katoomba and Blackheath. In spring and summer, troughs forming to our west (the dotted lines on the TV weather maps) often bring our storms and showers as these troughs drift eastwards. Remember though, nature doesn't always go by these rules, that's why the weather is so much fun!
Also, television and radio programs are generally not the best place to get your forecasts from as they often greatly abbreviate the forecasts issued by the BoM, sometimes to the point of sounding like another forecast altogether. Many of the presenters are also not well trained in meteorology, although some are okay. Graham Creed on ABC TV is the best by far, IMO, as he has a real love for the weather and has good meteorological training and forecasting skills.
Footnote: It is certainly possible for you to more accurately predict the onset of storms/snow for say Blackheath or other towns but this requires a reasonable grasp of the computer forecasting models and some understanding of upper air dynamics. Also, topographical influences (terrain variations like mountains and valleys etc) can significantly effect storm and rain development. If you are really this keen, I suggest you view the links at the top of this page or head to Weatherzone Forums, where you can fraternise with other weather nuts! :)