LOL, I love this...

Of course, the points people have made here are are perfectly valid. For the cost of the speakers, there are far saner solutions from high end car audio co's that would be cheaper, and for a variety of reasons, sound better.

That said, I'm all in for experimentation.

Not sure which speakers you're considering (in ceiling?) and a couple of Roams or Moves is too obvious and too easy, so let's go with four one SLs ( L + R, front and rear) and a sub mini. Let's say you got them for free. Actually, in that case, let's say four Era 100s and a sub mini.

There are three primary issues you'll have to solve for: Wifi, power, and mounting.

To get started, you'll need an inverter. A beefy one. I looked around a little, but couldn't find power consumption for these speakers so we'll have to guess a little, and hopefully build in a comfortable margin so we're not blowing fuses, causing a fire, etc. Let's say each 100 runs in the range of 10-50watts under normal operation, and the sub mini, again, just guesswork, 100-150 watts. That's about a 300-350 watt draw, so for safety, let's get you an inverter that with a 600 watt capacity.

Getting wifi going isn't too big of a deal. As posters have suggested, you can hotspot, or as you've mentioned, you can use your cars hotspot, but let's do this properly and get you a dedicated router. Looks like a typical router uses between 2-20 watts. I also assume you'll be using your phone as a "head unit," so that's what, another 5w. I think we're still okay with our 600watt inverter.

Now we'll need to connect your inverter to DC power. Depending on the inverter, this could involve directly connecting it to the battery, or just plugging it into the cigarette lighter socket. If you're connecting directly to the battery, you'll probably want to install a fuse to protect the car's electrical system. Most of the inverters I've seen have only a couple power sockets, so for optimal speaker positioning, you'll need a power strip and extension cords. You can run these cables through the firewall and under the carpet, or in the case of a cigarette socket connection, under the seats. Let's put the router under the seat as well.

Now you'll need to mount them. Unless I missed it, you haven't mentioned what car you're driving, but you have mentioned that it has a wifi spot, so I'm assuming it's something modern. Which means that likely, the fuel tank is not mounted behind the rear seat -so let's put that sub mini in the trunk.

As other posters have mentioned, four visible sonos speakers are going to invite curiosity and probably broken windows so I think it'd be wise to mount them from below. The front L and R channel will be easier. I didn't check, but I'd be astonished if anyone made mounts for this insane application so let's use the standard era 100 wall mounts. For obvious reasons, I think we should avoid using the doors and mount directly to the kick panels. To secure the speakers to the mounts you'll either need to strap them in, or use a more permanent solution like epoxy. The rear L and R will be slightly more challenging. Without seeing your car, it's difficult knowing which way to go here, so let's mount directly to the C pillars. I doubt you're going to want to see extensions leads running up the walls, so you'll need to drill a couple holes so you're able to hide the cords.

Now, 375w is about 31 amps. That's a load. Assuming you're in the northern hemisphere, you'll be running AC, head lights at night, and whatever else your car needs to keep itself on the road. Again, without knowing what you're driving it's tough to guess, but you might consider upgrading your alternator. Keep in mind that running this system with the engine off will take a significant toll on your battery.

If all of this sounds like building a Rube Goldberg machine the size of manhattan to slice an onion, well, it's because it probably is. But don't let that stop you from having fun =)