Another option might be to use a kumo wireless tag instead of the SmartThings arrival sensor. The range on these is a much longer. You can do an integration just with IFTTT, or @swanny has done a really good direct integration with SmartThings.
This has the advantage that you could put the base station for the wireless tag as close as possible to the driveway because you really only be using it for this sensor. It just has to be able to reach your Wi-Fi signal.
The tag themselves are fairly cheap, around 30 or $35, but you do have to also buy the base station which is about $60. So that might not be worth it.
The other issue is that while the Kumo tags themselves are quite nice devices, the customer service from that company is terrible. So it’s really hard, for example, to get a return authorization. But there are a lot of community members using the tags and they do yplike them.
Anyway, I wouldn’t ordinarily bring that up but with the weather situation you’re dealing with it’s always good to have alternatives. The other thing that concerns me is that rain or snow themselves will reduce signal and that can be a problem with the kind of driveway detection you’re talking about. It’s not just the cold matters.