I grew up ice fishing in the Midwest, so I know a few things about when the ice is safe to walk on. But driving a vehicle onto the ice, while possible and I've seen and done it before, is a more precarious thing than just walking across it to get to your tip-ups or shanty. It's something you need to learn how to do safely, and that all comes down to ice thickness.
Recently, a group of six snowmobilers messed around and found out that the ice on Lake Vermillion in Northern Minnesota wasn't thick enough to support their snowmobile's weight, plunging into the icy depths, and having to be rescued before the worst could happen. Of the six, two were children, according to local reports.
But the whole thing got me thinking about how I once learned about ice depths and weight back in the day, and figured this event was a good-enough time to remind everyone else about the dos and don'ts of traversing the ice using vehicles. So let's get into it.

I snagged this handy-dandy graph from Montana Fish and Wildlife, as it's exactly what you need to know before touching anything covered in ice. As you can see, it's broken down by ice thickness in inch-by-inch increments, and showcases some of the common usecases of a frozen lake or river. Apart from the duckbilled dinosaur, obviously.
But under four inches, and you really need to stay off the ice. Even at four inches, you have to be careful, as ice doesn't uniformly form, and there could be patches where the ice isn't as thick as others, especially around the edges of a lake or river, or directly in the middle. And as you can see, the time when you can use a snowmobile on the ice is around 7+ inches thick, though, again, you have to be careful as what occurred in Minnesota was that the snowmobilers didn't see a pressure ridge, i.e., a crack, and fell through.
According to the local Bring Me The News outlet, "The crash was reported around 6:20 p.m. Sunday near the Tavern on the Bay in Tower, Minnesota, with police receiving a report of 'multiple snowmobiles' through the ice near a pressure ridge 'that had formed on the marked trail.' Four adults and two children were involved, but all were able to make it back onto the ice with the help of patrons and employees of Tavern on the Bay. Five of the six were taken to area hospitals for exposure, with no other injuries reported."
Personally, I always waited until around 8 inches thick, and the weather being cold for a sustained period, as warm fronts or ups and downs can change the ice's formation in different spots, which can cause structural issues. Likewise, while I saw other folks do it, you couldn't pay me to get in a truck or car and drive out onto the ice. Yes, at a foot, you're probably fine. But even I have my lines I don't cross.
The local Sheriff's office reminded folks, "The sheriff's office would like to remind those out enjoying recreation on our area lakes to use caution at all times and ride responsibly. Be aware of your surroundings and avoid any questionable areas on the lakes with unknown ice conditions. If you encounter issues or hazards on the marked trails report them."
So, again, check the ice depth and use your best judgement. It's not worth the risk of you drowning in an icy lake just for some early season snowmobiling.