How is it possible for temperatures to be too cold to snow?

It is not. It can be too dry to snow but not too cold.

Technically it is never too cold to snow, but it can be too cold to snow much. The colder the air is, the less water vapor it can hold. Thus very cold air simply does not have much water vapor and likewise cannot produce much snow.

Thundersnow is a result of an atmosphere that is both cold enough to produce snow, yet still having sufficient instability to allow the clouds to grow tall enough that the large number of snowflakes striking each other can generate the needed electrical field for lightning.