You mean that car passed the yearly safety inspection ( MOT as we call it in England) ? It would have failed many years ago over here, you would have started with an advisory, then get it done before the next test, then fail. Don't drive the car.
When I bought my car new I had waxoyl treatment.
You could knowing the state of your roads, weather etc had it done then once a year ( summer peferably) using old engine oil paint the subframe. When we get snow ( which is once every 5 years) I put the lawn sprinkler underneath on the hose pipe and pull it from one end to the other of the car, which doesn't take any effort.
I cannot say I have much sympathy or you if you haven't inspected the car underneath since you have owned it, knowing the local conditions.
Our cash strapped council will grit the roads with salt every time they hear there is going to be a frost. It may have been dry for a week , so I am not sure what they are expecting to freeze.
On the odd ocassion we have snow, just enough to whiten the ground, it has usually disappeared by lunchtimes and within 30 minutes on the main roads, but you still have people calling in to work to say they are snowed in, despite them driving a huge 4x4 or SUV. It amazes me the mentality and lack of driving skills the younger people have. I have driven in 4"-6" of snow in a 1980's Mini and thought nothing of it. Not a soul on the road, freezing temperatures crossing the ridge of hills that run down Northern England, never got stuck once. Great fun it was. Fortunately it didn't snow any more* and was a clear night.
I don't think you have a chance of claiming anything.
In Japan I understand they ship the domestic cars to Australia/NZ after a couple of years so the rusting is never experienced, plus they don't treat the underbody either like European manufacturers.