Most true 4wd systems should not be used on dry pavement. That's because they have a transfer case which locks the front and rear axles together when engaged. When you try to turn, the axles need to rotate at slightly different rates. With the center locked, the drivetrain will either bind up and have extra friction (lower MPG), or the tires will have to slip a bit, or both. You can use 4wd when the roads are covered in snow, but in mixed conditions where there are dry patches and snowy patches, it might not be the best idea.
All wheel drive doesn't have that problem, and it's engaged all the time. It's fine to use in all conditions. The only time when you might need 4wd instead of AWD is getting out of a deep snow bank or something like that. Also keep in mind that not all AWD systems are the same. Some work continuously, like Subaru's, and some work some of the time, like Honda's. Most or all of them are good enough for winter driving, especially considering 2wd is enough too.
A 4wd vehicle in 2wd mode won't get significantly better mileage. There's a tiny bit less friction and nothing to bind up, but you still have the extra weight of the 4wd parts, and you are still driving a big SUV or truck. You can find AWD on smaller, more economical vehicles.
One exception is the 4wd system on some older Toyota trucks. The 2003-2009 4runner, for example, has a center differential that's used in 4wd mode, so you can use it all the time like AWD if you want. The traction control system manages sending torque to the appropriate wheels as necessary. If you need more traction, you can lock the center differential and you have essentially a traditional 4wd system. If you need even more traction for extreme off-road driving you can get a locking rear differential too.
There are hidden costs to AWD and 4WD. For example you always need to have matched tires, so if one is severely damaged you will need to replace all four. And there are more parts to break and more things that could go wrong.
If you do get a 2wd car, it might be a good idea to get one that has a traction control system or limited slip differential that can control wheel spin. That way if you are stuck with one wheel on a slippery patch, there is some chance of some torque going to the other wheel to get you moving. Otherwise you have, like my car, what I like to refer to as one wheel drive!