NB: Please read the Learn to Forecast and Observation Skills links above if you really want to learn the nuts and bolts of storm and weather forecasting. Special thanks to Anthony Cornelius and Jimmy Deguara for these excellent guides. This approach is what most skilled forecasters (professional and amateur alike) use for day to day forecasting.
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!
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 my 'Cold Climate Information' link on the main page and also my 'Other Weather Sites' link there and head to Weatherzone Forums, where you can fraternise with other weather nuts! :)
Stop Press: Anthony Cornelius has produced an excellent document on forecasting thunderstorms, here.