Remember to keep it simple, or it'll seem overwhelming and you'll get nothing done. Your idea of a tractor is great, but then you talk about a bucket on front and blower on back, and then you're moving to put beet juice liquid in the tires. I say slow down.
You just moved half way up the US coast to Maine. You bought someone's vacation home, implying that it may not be in a location with "all" the city/suburban services. You moved in at a time when that region enters it's toughest conditions with little experience or preparation. Don't try and tackle every problem at once.
1. Check with your neighbors, library, or Pennysaver flyer for plowing and sanding service. Hire them. They'll plow your drive and sand for you. Maybe they're even looking for some seasonal help and you could pickup some beer money.
2. Find a local truck & trailer center, or a u-haul center, and get a plow attachment for your duelly pickup.
3. Get in the habit of checking weather daily when you come home, and decide it the chains are needed for the next day (do that every day). Get used to driving slower.
4. Get your wife mobile. She probably feels equally overwhelmed and trapped. If new studded tires are out of $ range, check if your local tire guy can set her up with some smaller (undersized) used tires and get some close fitting cable "chains". Back in my day we called em Euro chains or s-chains.
5. Pick up a yard or two of sand at the Sand&Gravel. Mix each yard with a bag of salt and dump it on a tarp, then cover it with another tarp. Don't let it get rained on. Use some every day everywhere there's ice. Buy a good welcome mat to keep the dirt outside.
6. Plan on getting up an hour or two earlier every day to do the chores that come with living in the country. That means going to sleep earlier. ;-)
7. Find fun things to do with your wife in your area, so you are not so homesick every time the weather forecasts another 6-12 inches. XC skiing is relatively cheap and you can take your dogs with you. Again, the local library is great for those local resources.
OK, now it's time to tell me to shut-up and hit me with a snowball.