Originally posted by: Rubycon
There's a couple things at work here and a few things to consider. If your ductwork is "tight" as in minimal leaks (no panned plenums, etc.) then closing off the vent will afford higher pressure on the supply trunk and deliver slightly more air to the neighboring vents. It should not be detrimental to the indoor blower fan - most residential "squirrel cage" blowers actually "load down" under a higher static discharge pressure. Thus if you're measuring amps on the motor it will go DOWN as the pressure goes up. (from closing off vents)
With a heat pump it's important to maintain airflow over the indoor coil above the minimums as this component in the heating cycle is now the condenser. Higher condenser temperatures equal higher head pressures which means the compressor will pull more amps negating your savings. Also too high a head pressure will trip the high head pressure switch and if this component is not an auto resetting type you fall back on auxiliary heat which in the case of strip heaters - is expensive!
As for air balance, variable air volume (VAV) using pressure sending units downstream of the main fan, fan vortices and variable speed fans* are in use due to complexity of maintenance, setup, expense, etc. If that was the case you could just zone off that area and be done with it.

[* variable speed fans are in residential settings but not as a component of VAV control.]
Finally if there are outside walls that have pipes carrying water that sits still; freezing is a definite possibility. Again, this really depends on your climate.