I think that this is completely wrong. The ability to make snowballs is related to the wetness of the snow. Dry snow is not sticky at all, whatever the temperature, and I think the amount of pressure needed to even partially melt it is beyond what you can achieve with your hands. When the snow is wet, no pressure is needed: simply taking a snowball and lightly putting it on fresh snow is enough to make additional stick to it.
There is often a link between the wetness of the snow and temperature: wet snow usually falls when temperatures are close to freezing. But I have often seen dry snow when the temperature is just below freezing. Likewise, old snow that has been on the ground all winter is rarely sticky, whatever the temperature.
Caveat: all this is based on personal experience of having lived nearly all my life in regions where snow is abundant. I have never dug deeper as to what actually makes snow wet and dry.