Balconies are often neglected in the winter, since they are rarely used. Accumulated snow can weigh them down, sometimes damaging their integrity, especially wooden balconies. Because of this, some condo and apartment complexes mandate their residents remove snow from their balconies. While not always the easiest task, there are several methods that effectively remove snow from balconies.
Examine the area under your balcony. If there is a sidewalk or parking lot, you should not throw the snow over the balcony unless you plan to remove the snow from the ground as well.
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Shovel just a little bit of snow and toss it over your balcony, checking first to be sure no one is in the way. See how far you can fling it. If you end up hitting the balconies underneath, this is not the best option for you. If you can safely throw it several feet out from the building into a safe area, then remove the snow from your balcony in this manner. You may also be able to effectively sweep it away.
Shovel the snow into 5-gallon buckets or other large containers and dump it in your bathtub to melt with hot water. This is a slow process, but may work well if your circumstances don't allow you to dispose of the snow outside.
Melt the snow. There are many products sold to melt snow and ice, but read the label carefully to verify it is safe to use on concrete or your balcony material. Alternatively, melt the snow with warm water with a little bit of table salt mixed in -- about 1 tsp. per gallon of water. After melting the snow, improve traction with sand or kitty litter, if necessary. In the spring, sweep up the sand and kitty litter and discard.