Is it necessary to protect a (half full) propane tank from freezing temperatures?
Actually, no.  You need to keep it exposed to weather to keep it warm.   Yes, you heard right. 

Or any other heat source would do.  

Propane is stored as a liquid, but used as a vapor.  As you use it, it must convert from liquid state to vapor state (i.e. Boil). That requires it absorb energy, its latent heat of vaporization, from its surroundings (i.e. the liquid propane in the tank). This will make the liquid even colder than ambient air.  You may have seen propane tanks condense water or "ice up" when in heavy use. That's because they are colder than ambient.  This is that effect.  

If the liquid propane can't absorb its latent heat of vaporization, it won't boil. So when the liquid propane falls below its natural boiling point, then you will have no vapor pressure at all, and your propane accessory won't work.  Much like a boiler gives no useful steam if its temperature is below 212F (100C).  

You rely on heat transfer from outside into the tank to keep the propane "warm enough" to boil on its own.  Trouble is, heat transfer works best when there's a big temperature differential.  When the outside is already cold, heat transfer is slower.    You want the opposite of insulation, you want a heat exchanger to speed it up.