Have a 2000 Chevrolet Silverado with a heating/AC issue I've never encountered.  For some reason the system does not blow anything at all out of the vents (nothing at all - no cold or hot air) until I hit about 20 mph.  Once it starts blowing the air is ice cold and the heater works fine.  I can slow down or stop and it will continue blowing just as good.  The issue only occurs when I first start the vehicle until it kicks on when I hit 15 - 20 mph.  

Anyone know what's causing this?  It seems like it should be an obvious problem, but I know nothing of HVAC systems and my Googling hasn't been successful.

Sounds like a stuck blower motor, or bad connection to it.

Blower resistors are a common problem on those trucks. Take the cover off on the passenger side and unplug the resistor and you will see melted stuff. Replace the resistor and pigtail and enjoy blower speeds again.