What extreme measures might a pilot take to avoid extreme weather?
Any which the pilot thinks is more dangerous than the avoidance measures?

If you were driving at 100mph towards a wall which you reckoned had a 90% chance of a head-on collision, or could attempt to turn which had a 50% chance of throwing you off a cliff, which would you choose?

Any decision the pilot makes will be made on the basis of "Taking this action is a better option than not taking it".

The main weather which would likely cause this would be high enough levels of icing to be dangerous, or such severe turbulence that the pilot believes the plane will be "upset" enough to throw it out of the performance envelope. A combination of these may be present in a severe storm.