Cold Weather
Cold itself is nothing to worry about unless your ignition system or battery is weak. Stay on top of your ignition system and battery health, and temperatures as low as -20F will still be just fine for an RX-8 to deal with. Cold weather will increase the risk of flooding with a weak ignition or weak battery faster than warm weather. You will also want to have a lighter 'cold' weight oil than during hot months. Target a 0w## oil, like 0w40, to increase the speed at which the oil begins circulating through the oil system.
Snow driving is the main other concern. However, it is all about the tires.
If you drive on snow or ice on summer tires, you will crash, get stuck, or otherwise have significant trouble with a great risk of peril.
If you drive on snow or ice on all seasons, it will be touch and go with careful driving, prepare to be stuck periodically, but you may get through ok as long as conditions aren't too severe.
If you drive on snow or ice on winter tires, rule the road and enjoy up to ~4-5 inches of fluffy snow on the road surface before you get stuck.
Also throwing in that I drove my RX-8 as my only car through 4 New England winters. The car you have doesn't really matter for anything but sheer ground clearance. FWD vehicles and SUVs are more likely to have more winter friendly tires on OEM, sports cars are more likely to have OEM summer tires, and this is where the major difference is. As long as you have ground clearance though, the RX-8 with winter tires will out-drive any SUV or jeep on OEM all season tires. While I was in New England, my work was on a hill, the highest point in the state, and each winter I regularly climb the last steep hill into work, often winding my way around stuck SUVs and trucks. I was the only one in my office to make it to work every day if the office was open. My co-workers with their FWD cars and SUVs were frequently getting stuck or couldn't get out of their driveways. Proper winter tires makes THAT much of a difference.
Additionally, the attributes of the RX-8 lend themselves well to traction in snow. The RX-8 is low torque, more weight over the rear than most big engined sports cars, and a great set of driver aids. My only concern for driving it in the winter at all is the salt. The only time I got stuck was when it started dumping snow and the plows were not sent out until literally half of the state was stranded in gridlock and ditches and the snow was simply too deep to push through. The low ground clearance was a bonus though, I was one of the first stuck, and thus got one of the only tow trucks. The tow truck got stuck on my street about 30 yards from my driveway after dropping my RX-8 off. Even he needed the extra weight at that point.
Snow driving is the main other concern. However, it is all about the tires.
If you drive on snow or ice on summer tires, you will crash, get stuck, or otherwise have significant trouble with a great risk of peril.
If you drive on snow or ice on all seasons, it will be touch and go with careful driving, prepare to be stuck periodically, but you may get through ok as long as conditions aren't too severe.
If you drive on snow or ice on winter tires, rule the road and enjoy up to ~4-5 inches of fluffy snow on the road surface before you get stuck.
Also throwing in that I drove my RX-8 as my only car through 4 New England winters. The car you have doesn't really matter for anything but sheer ground clearance. FWD vehicles and SUVs are more likely to have more winter friendly tires on OEM, sports cars are more likely to have OEM summer tires, and this is where the major difference is. As long as you have ground clearance though, the RX-8 with winter tires will out-drive any SUV or jeep on OEM all season tires. While I was in New England, my work was on a hill, the highest point in the state, and each winter I regularly climb the last steep hill into work, often winding my way around stuck SUVs and trucks. I was the only one in my office to make it to work every day if the office was open. My co-workers with their FWD cars and SUVs were frequently getting stuck or couldn't get out of their driveways. Proper winter tires makes THAT much of a difference.
Additionally, the attributes of the RX-8 lend themselves well to traction in snow. The RX-8 is low torque, more weight over the rear than most big engined sports cars, and a great set of driver aids. My only concern for driving it in the winter at all is the salt. The only time I got stuck was when it started dumping snow and the plows were not sent out until literally half of the state was stranded in gridlock and ditches and the snow was simply too deep to push through. The low ground clearance was a bonus though, I was one of the first stuck, and thus got one of the only tow trucks. The tow truck got stuck on my street about 30 yards from my driveway after dropping my RX-8 off. Even he needed the extra weight at that point.