You guys need to give this guy a break. He comes in here asking good advice on a cheap way to store/protect his tractor and now he gets grilled about his wife. I do not let my wife make my decisions for me but we all have different personal arrangements. Lots of women need a man to think for them but some men need a woman to think for them just the same. And his wife is willing/capable to maintain things and plow snow while he is away working, sounds like she's more than just a lil primpy female that is afraid of getting her hands dirty. Those have their place in life as well but that type is not for me. But we are not here to judge or catagory our wives.
It has been said that storing your tractor out in the weather is ok. I totally disagree with that statement. Moisture will get in the crankcases and sun will deteriate rubber. We all should know this. And a tractor covered in snow is not one that I'd want to use to plow same said snow. So the OP is right in thinking he needs a shelter or cover to protect his investment.
If I were in your place and I could afford it, I'd go the aluminum carport route. It will be more sturdy and last for years where a portable barn in a box or fabric storage might not take the weight of the snow if it gets really deep. And if you are plowing it, I would think that may be a possibility. And after you get your barn built, you'll still find a use for it or sell it. And have the installer place it in a way to put the north side with a wall all the way down to the ground or finish that side with plywood, probably just as cheap to get them to do it with the same covering. Most winter wind, rain and snow comes from the north in my area and I assume it does for you. You may even get them to go full sides on both sides if money is no problem. But definately get some kind of shed for it.
Covering with a tarp is better than nothing but you need to have a shelter if possible. A tarp holds moisture and when the sun comes out moisture rises and hovers in the tarp, not clearing away like in a shelter. And a tarp makes the job of using the tractor not as easy. She'll have to remove and replace it out in the cold and that definately isn't just getting on it and going.
Now the easy way would be to give the wife a little lesson in driving in low gear, low idle, in close places and park it where you first intended. Tell her you know she can do it and make her proud to be able to do it like the big boys do...lol. Got to build her confidence if you think she can do it. And spend that money on a heated cab...she'll think that would be a pretty good trade. For the same money, you can protect the lil wife from the weather and let the existing porch protect the tractor. And sometimes you just got to tell them how it's got to be.