In bad weather they are similar to any other multi, very stable. But with the advantage of being able to lift all the underwater foils, leaving you with a huge raft, drawing less than 300mm/12”. This would be almost impossible to capsize by wind and wave action. Add a parachute anchor and it is even less likely.
Seaworthiness is as much about the crew as the boat. A well rested crew that is not scared or endangered will make far fewer mistakes than a tired one who is afraid to go on the foredeck. Harryproas are very safe and easy to sail. The crew never leaves the area between the beams and the hulls, never has to remove/replace sails and can sail the boat from a dry, sheltered position.
Most bad weather problems are caused by the crew becoming tired or scared. If possible, before it gets to this stage, drop the sails, lift the rudders, go below and wait till the sun comes out again. This is far more pleasant and less likely to result in problems than trying to sail when you are cold, wet and tired. In extreme cases or when you do not want to drift too far, towing a parachute anchor will keep you safe and minimise drift. Deploying and retrieving a parachute from the centre of a double ended boat is far easier than from the bows of a cat, tri or mono.