I was in a similar situation last year- fairly limited budget, long gravel driveway (only 700'), in snowy NW PA. I ended up with a Wheel Horse 520H. I didn't get this setup until about 1/2 way through the winter and haven't had it a whole season, but as far as snow removal, it works fine. It's not supper fast, but I didn't have the money for the fast solution.
Although Wheel Horse tractors are no longer made, the ones they did make were very well made, pretty easy to work on, and more capable than I expected. For $1000 I got a 20HP gas tractor with a 60" mowing deck and a dozer/snow blade for the front. I bought a set of chains for the rear tires and does a pretty decent job clearing the driveway. I really bought it for snow removal (with a front mounted blower on my wish list) but the mowing deck has proven quite useful so I got rid of my other mower.
It's admittedly limited- with a plow on the front you can't really get too far behind the accumulated snow or your in trouble- part of the reason I want to get a blower. Parts aren't hard to come by but I haven't really needed any. Basic stuff (filters, plugs, belts) can be found locally and don't seem un-reasonably expensive. Since it's gas, and I don't have a heated garage, I don't have to worry about starting even in cold weather.
Mid-mount grader blades are available for them but I've never used it for that. You can push a certain about of dirt/gravel with the snow plow but I'm not sure how well it would do for repairing a washed out driveway. There are other attachments available for it. They have a side-mount PTO that will work with tillers, sickle bar mowers, even front-mounted mowing decks. The series I have does NOT have a rear 3-pt lift/PTO.
Maybe something to consider, especially if you don't have any other uses for a larger more expensive tractor.