I had to shovel from the house to the driveway before going to work. So I got HeaTrak mats for my walkway and steps plus carpeted mats for in front of the doors. Due to how we had to configure them, we had to buy extra cable extenders. It was over $1000. for the initial purchase. We've had them for about 6 years and have had to replace one power supply, both carpeted mats and 2 of the walkway mats last year. One mat is on patio pavers and the ground will heave on either side of the mat because you are heating the ground under the mat. I would think your gravel driveway would heave too. Water does sit on top of the mat until it evaporates or it will run off the sides of the mat. If there is a lot of snow, snow will sit on top until it eventually melts but it does melt. It is nice that I'm just running through water and not snow getting to my truck in the morning.
They now have driveway mats ($1600 for one 2' X 20') if you decide to go this route make sure you can use on a gravel drive way.
https://heattrak.com/collections/residential-mats