The whole point of the term "severe" in relation to icing is
The rate of ice accumulation on an aircraft is such that de-icing/anti-icing equipment fails to reduce or control the hazard. Immediate diversion is necessary.
from the NOAA website.
So flying in Severe icing is unlikely to be a long term problem as you have the aerodynamic efficiency of an iceberg.
As for freezing rain specifically if you look at the hold over times for "light"
Type 1 : 02-05
Type 2 : 10-30
Type 2 : 05-40
times in minutes depending on OAT. So there really is very little protection avaliable, and as soon as it goes "moderate" then there are no holdover times and your grounded.