Outside Winter Storage..?

Might as well leave the tarps off - when the temperature varies, that's when the condensation will happen and without airflow that moisture has nowhere to evaporate to. Carpet is like a sponge - I wouldn't put it anywhere near metal. Use rubber blocks, or cut some pads of horse stall mats instead.

You could shrink wrap the whole thing after placing a bunch of desiccant inside and it would probably be OK under a tarp. Even then, it'll have to be done while the dew point is relatively low compared to your lowest winter temps and the desiccant will have to be pretty fresh in order to do much good - and the wrapping accomplished soon after the desiccant is opened up inside the car. This still won't do much good for the engine compartment area though!

If you have an area where temps don't vary much (out of the sun, to prevent warm air sucking up moisture that will get wrung out later) and use a double walled 'carport' style fabric shed, it could be OK as well. If you've got a really good spot where temps remain relatively constant, a single wall might be OK. You'll still want to be able to run a fan in there though to exchange air in the event of moisture build-up. Get one which is U-shaped so that any potential condensation can run down the sides of the cover rather than drip on your car. There's several out there which can withstand a couple feet of snow. If in doubt, reinforce it some.

If tarps are the only thing in the budget, I'd keep the car in the garage and tarp it while you do your projects around the car.