It very seldom snows enough in Jindabyne for the snow to settle. Even at Thredbo the village doesn't get a lot of snow.
Maybe try googling Sawpit Creek. It's between Jindy and Perisher, most of the time it's below the snowline but it is more likely to have snow.

If you find a hill with snow on it you can toboggan but most of the hills with snow are difficult to park by. Dead Horse Gap has a car park and is just past Thredbo.
I think you can toboggan for free at Selwyn if you hire a toboggan from their shop (don't quote me on that). If you just want snow play and maybe give skiing a try I would think that Selwyn/Tumut would be a better destination for you than Jindabyne and Thredbo/Perisher.