It's best to select freshly fallen snow that's nice and white. Simply shovel as much as you can into your receptacle and bring it somewhere where the temperature is above freezing. This doesn't mean that you have to drag it inside your home, since you don't want your little ones playing with the snow, but a garage or storage area would work. If you're working with a two container system, one to get the snow and a larger one to thaw it, then you'll probably have to fill it a few times in order to get enough water, as snow takes up more space than water.
The large container can be kept as a watering base, to fill up your watering can. With all of this snow, it's time to get some use of it. There's good news: you'll probably never run out of snow this winter. You work a similar system if you're living in an apartment and you've got a balcony. Simply gather as much snow as you can and put it in your watering can. Once it's melted, you can water your plants efficiently.
We'd stay away from snow that's not white, maybe from salt or sand or other contaminants that could harm your plants. This is why we suggest using the snow from your backyard. Remember that the average snow to water ratio is 10:1, so it will take a lot of snow to make water.