I have used a snow thrower on gravel, it works, just set the "feet" on the bottom to about 1" so it will leave some snow behind.
For a large drive way you can't beat a tractor. A cheaper way might be a 4x4 quad, but you are still looking at a couple grand. You can get a great snow blower for $1,000 that will make quick work of that too. Just depends what you want to spend. You could also get an old truck for like $1,000 with a plow, but then you will have maintenance issues and it will always be broken when it snows!