Does the mounting orientation or side of a heat-sink matter?
The mounting direction of the heatsink is not important. Only the airflow is.


If you use natural convection then the airflow should be able to rise from the lowest part up for all the fins of the heatsink.
If you use forced convection then the airflow should be forced along all the fins of the heatsink.


In computers you can even find processor cooling with a ventilator on top and forcing the airflow down over the fins of the heatsink. 

Therefore only the total approach determines the limitations of the heatsink position.