I had to do that at times when I had more than 1 collector car. And it really bothered me knowing my '69 GTX and/or "69 Super Bees were sitting outside under high quality car covers + heavy duty tarp over that. No matter how I did it, moisture and/or condensation would get through to the exterior paint. But, they did an ok job keeping moisture away from undercarriage, interior, and engine bay. I only did it for 1 year at a time so hard to say what the long term effects would be. With a large tarp as the outer layer, your tires/brakes and undercarriage are protected.
If I had to do it again, I'd probably set up a fairly durable portable car port to keep most of the rain/weather away. Some fairly rugged, light-weight units might only run $200-$300. In the heavy snow though some of those just might tip over or lose the roof if you don't get the snow off quick enough.
I'd be less worried about the winter where a tarp over a car cover could be easily swept after each storm. And condensation is not much of an issue from 10-45 deg F winter weather in NJ. During the months of April to November you have to be quick to get the cover off to dry from time to time. I'd put some plump old pillow between layers to help the tarp drain off the bulk of the water. I had a $200 California Car Cover and a 30ft x 20ft tarp. Even though they say the Car Cover is "all weather" and "breathable" they let considerable water in and take a while to dry once wet. When I went to overnight car shows at Carlisle or Englishtown, I always brought both layers. I think a breathable car cover is best or you end up with pockets of condensation that won't go away very quickly. If you want a second cover to put over that as waterproofing, that's fine. Any time I was expecting good weather for a few days I'd expose the car cover, let it dry, then expose the car for a bit to ensure it dried everywhere. My best car always stayed in the garage.
Having done it both ways without a portable car port, I'd say it's quite doable. At times it's a pain to keep up on everything. But, that's the price to pay if you want a collector car. Fwiw, my latest daily driver car has been sitting outside for the past 8 years. And I've seen fairly little degradation on the paint, engine bay, and undercarriage. Constantly removing and installing covers/tarps can put more lines in your paint, especially when that cover is not 100% perfectly free of grit, sand, debris, etc. You can always get a fabric liner of sorts that goes under the car cover for roof, hood, and trunk lid protection. But over time, the car picks up dirt from the air and/or road....and some of that finds its way into your covers. I like the portable car port idea though and probably would have done it if I had no garage. They sell car "bags" that you can drive into for winter for 4-6 month storage. Never liked that idea since I try to get my cars out at least every 1-4 weeks all during the year...if the roads and weather accommodate.