i'd buy a fabric cover directly over it, then cover it with a blue heavy duty tarp tight to the tractor. one more tarp on top of that tented out on the sides staked to the ground so water runs out and away. that should keep it good for the winter.

Tarp material is important. I'd rate all-weather mouse bait placed on the mower deck and perhaps under the hood as being more important. Bait Blocks work best. Best to check for signs of nibbling periodically by lifting the tarp. Dead mice in a hot engine are potentially a really bad problem. Live mice jumping out from under the hood and then finding the tractor will not start can be much much worse. Mice like to chew...wires for instance.
Anyways, buy a thicker (6 to 8 mm tarp) as it will last longer. Make sure to "tent" it so that water,snow and ice run off and do not pool on top of the tarp.

Has anybody ever seen a tarp that you could spread out, park on top of, then another tarp that zips around it to make a weathertight seal? Kind of like a sleeping bag for a tractor or snowmobile. Seems simple enough. This could be my big break.

I think I'd stuff something in the exhaust pipe to keep mice out. Steel wool?

See link below. Used for classic cars and collectors.

Here is a link that might be useful: Car Capsule

Is this a closed tarping (storage) for the full winter or are you going to try and use the tractor periodically?

try mothballs or flakes in a sock or stocking and stow it under the hood to keep the mice away...

Iam retired and restoring old sports cars is my hobby.
I only have a 40' x 40' work shop so it always seems that some cars must wait there turn setting outside.
I cover all cars with a cotton cover then make my own "bubble" by placing top and bottom tarps and rolling them together at the bottom and securing them with tie wire.
I tried before with just a top tarp and the oxidation from the ground mositure was unbelievable.
My cure for the rodent problem is dryer sheets in the engine,interior and trunk,,,seems to work.

There's nothing like getting situated in the seat, starting the engine, and then having a mouse jump from the hood onto your lap.

Been there, done that! I Went to a friends home to get his tractor running. After much work, i finally took off the flywheel cover and---WOOO-Haw--there was Momma mousie and 3 of her off-spring, just finishing a tasty repast consisting of the insulation on the spark plug wire!
So, a size 12 boot, and some scampering around by momma, to no avail, and the sending of said off-spring to their heaven, i installed a section of rubber gas line over the plug wire, and that solved the problem! Momma was also insulating the area with some pink fibreglas insulation from the shed walls, so watch for that stuff, too.

I would try to get it up of the ground. A couple of pallets would probably work for most L/G tractors.

I guess I would put a piece of heavy plastic (visquene) over the tractor, but only hanging slightly down the sides. The tarps on tops of that, Tarps breath which is good (and why you want the visquene open at the sides) but the plastic will prevent moisture penetration.

I agree completely with Mr. Wheelhorse. It is important to get it up off the ground and to put the plastic under the tarp. Do not wrap the tarp or plastic to the ground. Let there be open air, 6 inches or so, pull the tarp out and fasten it down much like you would a tent. The air needs to circulate to keep the moisture out. Good luck.

I keep hearing you talk about mice. I have had my lawn tractor almost chewed up by a rat or rats. I live in the country and I parked it in a small shed that was just big enough for the tractor. I figured this was surely better than having it set out in the weather. They chewed all the rubber from the steering wheel. There was nothing left except the little metal rod in the middle that looked like a steering wheel. They also chewed up all of the wiring. A couple of years later I got a new JD and I parked it outside in the weather for 3 seasons. It certainly never hurt it sitting out. If I were you, I would just expose it to the weather. That's what I did. I'm just too scared of rodents chewing on it. If you cover it, they will come. They like a nice warm dry place.