Land Rover Defender, Freelander or Discovery.
Suzuki Jimny and maybe Vitara.
Jeep
Land Cruiser
All can go pretty much anywhere and aren't phased by much so long as you know how to handle driving in ice, mud, whatever. Though any vehicle can slide on ice, I one had my Defender 110 skid it's two tons about 30 feet when I gently touched the brakes - the culprit was black ice that was almost undetectable until I stood on it. Wasn't doing more than about 15mph at the time either.
One important thing with four wheel drive is to ensure there is a differential lock in the gearbox at least, or traction control that can handle having wheels spinning and re-direct the torque to the wheels that are gripping. You can actually be worse off with four wheel drive if that's absent.
In a two-wheel drive vehicle, if either of the driven wheels starts just spinning because it's lost grip then that spinning wheel is going to be getting almost all of the power from the engine and you're stationary. Four-wheel drive means that if any wheel loses grip and spins, that spinning wheel gets the power.
But if there's either good traction control or a lock in the transfer gearbox that goes a very long way towards sorting that problem out. There's always the risk you'll lose grip to every wheel of course, but when that happens it's time to get out the recovery gear.
Studded tyres do work to an extent, but aren't a cure-all. Snow-chains work better, but will chew up tyres and the road even faster than the studs will unless only used while on snow or ice you can't otherwise get a grip on. Either or both may or may not be legal to use depending on where you are.