WOW u got to love that kind of service AND CHEAP!
Thats what I would be most afraid of. Though the constant exposure to the elements would slowly take its toll. A cover would keep the rain, dirt and ice off the car but won't do anything for the humidity and dampness which will get into every corner of the car.
This is what will get you... Humidity with these cars kill them... the electrics corrode, rust is everwhere and the moisture will eventually get in your brake system... Find a garage, preferablly one that is dry year round. I've left my car out side for a couple of weeks, but I was using it all the time... and if your car is like mine.. it will leak around the top, windows, and where the windshield meets the body work...all it takes is one good down pour and you WILL have issues... when these cars were made, they were not made well, and were made for people who were supposed to be rich, and able to replace expensive parts on a routine basis... they were never engineered for 356 days use, or to be out in the elements. I know it sucks that a $2000 Honda will run for ever and you can let it sit outside 24 -7.... but it aint a Honda.... trade the 308 on an NSX... then you can let is sit out all the time ... no worries.
An alternative to a garage is one of the self storage units. Some are large enough for a car. Take a good look at the general neighborhood & unit. The unit's floor should show no sign of moisture/dampness.