Why is rain above freezing level (altitude) not always "freezing rain"?
The freezing altitude or $0\,^{\circ}\mathrm{C}$ isotherm is the altitude at which the temperature is $0\,^{\circ}\mathrm{C}$ in free atmosphere. This altitude varies and is usually only temporary as it depends on a number of factors.



"Iso0". Licensed under CC BY-SA 2.0 via Commons.

Freezing rain is a condition in which the water droplets become super-cooled (i.e. in liquid condition while below the freezing point of water) and freeze on coming to contact with cold surfaces. This condition happens when snow formed at altitude completely melts and supercools into large droplets.



Source: www.srh.noaa.gov

It can be seen that, to form freezing rain, both warm and cold layers are required. One reason for not encountering freezing rain above the freezing line is that the temperature does not rise above the freezing point of water. In this case, we get snow or sleet.



"Ice Storm Chart" by RicHard-59 based on image by J.R. Carmichael - Own work. Licensed under CC BY-SA 3.0 via Commons.

Thought the above figure is for ground level, it applies for other altitudes also. The phenomenon of freezing rain is dangerous for airliners as the water droplets freeze on coming into contact with aircraft surfaces and can cause loss of lift among other problems.



Post-flight image shows ice contamination as a result of encountering Supercooled Large Droplet (SLD) conditions near Parkersburg, WV. Source: icebox.grc.nasa.gov