I've never been a high mileage driver in my Morgan, usually around 3 to 4k miles a year (and a heck of a lot less this year), but I've always made sure the car is able to be driven whenever I want.
I would think it would be a shame if you drove your car in conditions that concerned you, but equally well I think that it would also be sad if you denied yourself the pleasure of a drive just in case the weather became adverse. I completely understand the concern with salt, but rain really isn't an issue. It really doesn't take long to put the hood up if it starts raining, after all. Don't be put off by all this 'never put the hood up' posturing, it's just an affectation. Nobody takes it seriously.
Nobody dies wishing they'd spent more time in the office, and nobody dies wishing they hadn't driven their Morgan so much.