Bernzomatic propane torch won't light properly
HOW IT WORKS

Torches are simple devices.  The propane is stored as a liquid under pressure in the tank.  The valve on the torch provides an exit for the pressurized liquid propane.  

When the valve is opened, the atmospheric pressure on the outside of the valve is less than the pressure required to keep the propane as a liquid.  The propane begins to change state from a liquid to a gas, pulling heat from the environment as it does so.  (This endothermic phase change is why the propane tank will frost up and feel cold when used for an extended period of time.  It is also why they often do not work in cold temperatures, as there is not enough ambient heat available for the phase change to take place.)

The pressure inside the tank forces the propane gas through the valve where it mixes with oxygen from the ambient air when it reaches the vent holes near the tip of the torch, and then exits the tip as a stoichiometric mixture ready to be ignited.

SOLUTION


There could be a blockage in the valve.  This could be caused by a piece of debris, or the valve could be frozen due to the endothermic reaction mentioned above. Clean or thaw the valve to fix.
The valve on the tank it self could be blocked/frozen, but this is unlikely as you tried an alternate tank. Let the tank slowly warm up to room temperature to fix.
The vent holes near the tip of the torch could be blocked, not allowing enough oxygen to mix with the propane.  Ensure these holes are free and clear to fix.
The ambient temperature may be too low for the endothermic phase change to take place.  This means that the propane exiting the valve is too dense to mix properly with the oxygen at the vent holes, so it won't burn when it reaches the tip.  Given the time of year and the problem you described, this is the most likely problem.  You will need to warm the tank back to room temperature in order for it to work.  CAUTION read the warning label on the tank before attempting to warm it. Do not place near open flame or excessive heat, as this could cause the tank to explode.