Update 3.10pm Tuesday
Essential Energy has restored power to 590 customers in Taralga today.
A spokeswoman said crews had also worked to reconnect electricity to 810 other customers that lost power across Goulburn and district as a result of the snowfalls.
"We still have 400 to go but the majority of those will regain supply tonight. The crews are working as quickly as safety allows," she said.
Update 11.30am Tuesday
Goulburn SES has attended 18 call-outs since 4am Tuesday.
Local unit controller Bob Bell said most of these were to large branches that had collapsed underneath heavy snow. They spanned Goulburn, Lake Bathurst, Bungonia and Towrang.
In Murray Street, Goulburn, a large branch fell on a car parked in a driveway, causing extensive damage. Another vehicle was damaged in a separate incident.
Mr Bell said a tree also fell down across Highland way at Tallong, blocking traffic.
Two teams from Collector and one from Goulburn, comprising 13 personnel are attending the call-outs.
A Goulburn Mulwaree Council spokesman said no roads had been shut but the snow was very heavy on Bullamalita Road. Rain is melting it but people are urged to exercise extreme caution in the area.
Update 11am Tuesday
Essential Energy has reported that 1800 customers are without power in Goulburn and district as a result of the snow.
A spokeswoman said crews were dealing with 47 incidents. Power has been cut to areas of Bungonia, Towrang, near Marulan, Quialigo, Middle Arm, wayo and Chatsbury.
Ten crews, comprising 40 personnel, are travelling to Goulburn to assist the local crews in assessing the damage.
The spokeswoman could not say when power would be restored due to the volume of outages.
People are encouraged to call 13 20 80 for more specific information and to report any other outages.
Update: 10.20am Tuesday
Police report that no roads have been closed as a result of the snow but traffic is still delayed on the Hume Highway north of Goulburn.
A spokesman said both lanes were open and motorists were taking it easy, "cruising at between 80 and 100km/h."
The snow is also heavy around the Lake George area south of Goulburn. Former Goulburn Mulwaree Council Mayor Geoff Kettle was driving past and said he hadn't seen a drop like it in many years. However it had started raining.
Traffic is also flowing steadily in that area.
The Southern Tablelands region has woken up to snowfall this morning.
The snow is still falling and has settled on the ground in Goulburn and parts of the Yass Valley.
Roads are being affected by the weather conditions and all drivers are asked to drive safely.
No roads are closed in the Southern Tablelands currently.
However, northbound traffic between Towrang and Marulan on the Hume Highway is slow.
That's due to snow and ice on the road.
Drivers are advised to expect delays and allow extra travel time.
Some 25cm of snow has been reported at Taralga.
Welcomed rain is continuing to pour across the region and will most likely melt most of the snowfall.
There have been 32 millimetres of rain reported at the Canberra Airport, 17mm at Goulburn Airport, 34mm at Braidwood Racecourse.
A Jerrawa resident reported 22mm.
The top temperature is due to be 13 in Yass, 9 in Goulburn, 7 in Crookwell, 9 in Braidwood and 12 in Queanbeyan.