The Visitor wrote:
There is the chance that the parachute will ice up itself; when deployed
in icing conditions. If long enough(duration) in icing conditions there
is a risk of collapse. Of course it will deploy but it is not made to
collect ice and function properly.

Thank you. That was my question ... not whether or not a parachute could
sustain an airplane with ice, but whether or not a parachute itself is
susceptible to ice and resulting failure.