I have driven my F(ront)WD Hyundai Santa Fe on plenty of logging roads in northern New Hampshire.
It is quite possible to get around safely.
I even know someone who owns an off-road Toyota Corolla.
If you are looking at roads that get graded on a somewhat regular basis, you should be able to drive ok.
Stay alert on watch for rocks protruding up and for dips.
There may even be small wash outs.
If you unsure about the spot ahead, slow down, maybe even get out and scout it on foot.
If you aren't confident that your vehicle can handle a section of road, be extra cautious.
Getting a tow truck to your location will take way longer than in town.
Don't ask how I know ;--) Look for gravel.
Think twice (or more) about dirt roads, especially if it has rained or there is rain in the forecast.
Gravel holds up well, mud will suck your tires in.
If you end up on a narrow section, keep an eye out for places to pull over if you need to either turn around or make room for an approaching vehicle.
What kind of activity draws you to unpaved roads?
I am an off trail hiker, so if I can't drive in as far as I planned, I am just starting the hike early.
outdoors.stackexchange.com/users/3426/orangejewelweed
I love going for off-road drives in my Audi Q5 with quattro (she's no asphalt queen!).
I think that you need to consider tires and ground clearance just as much as the drivetrain of your car.
Good tires intended for off-road will give you significant improvement over street-only tires.
I'm not saying you need to go full knobby on them, but make sure you at least get some crossover tires.
Second is ground clearance.
I find that this is most important for traversing gullys or small canyons (think of things like a dry river bed or something like that).
The ground clearance helps increase the number of angles that will be able to traverse.
In addition, ground clearance also helps with the exposure of the underside of the car to the elements.
A stock Toyota Corolla going off-road might find itself with a snapped oil-pan and that's never good.
Finally, do the research on your roads.
Look at topo maps of your intended route, talks to others that have done it.
And remember to have fun!
outdoors.stackexchange.com/users/3624/Unknown Coder
I used to have a Subaru Forester Turbo.
I crossed rivers, drove up on mountains covered in snow (no chains), 4x4 tracks where other "passagers" car would be struggle.
Driving up the mountain to the sky field, people where parking down the mountain while a 4wd was picking up people and taking up to the sky field.
I remember the guy saying, "you will struggle to get there" and I reply "that is enough for me" :)
The bottom line is, I knew the car and what I was doing (mostly :) ) and I have experience with Utes off road.
Driving off road, you go as far as you think you can.
You will build up experience and go further next time.
Just don't be silly to go to far and get stuck...
It might be a long walk back.
outdoors.stackexchange.com/users/3710/Desorder
I regularly drive my 2003 Honda CR-V AWD on forest roads here in New Mexico.
There isn't much gravel anywhere, generally it is graded dirt and rocks.
Some roads haven't seen any work in a year or two, sometimes more, but we don't get nearly as much rain as NH.
If it is dry, the real issue is ground clearance, which is pretty good in my CR-V - you just have to pick your way around the biggest bits.
The most exciting trip I did was with a group to go caving in the Malpais, south of Grants, NM.
This was in the spring, so the snow had melted, but the Malpais doesn't drain well, being a thin skin of dirt over the lava flows.
So, the roads were all mud (several inches).
One car in the group was FWD only, and it had to be towed through the worst because once the rear wheels started sliding sideways it would end up in the ditch.
When we encountered meadows they were covered in standing water, and you had to pick a line across the meadow and go for it, not knowing really what was under it.
On one meadow I was unlucky and managed to bounce down on a rock at some point, which took out my evap filter (which I had to get fixed later).
At one point, one of our 4WD F-350's got bogged down and had to get towed out - it was that messy of a road.
I'd say the CR-V performed very well.
All in all, I've been very happy with the CR-V and regularly take it down pretty nasty forest roads.
I'm not sure that I'd take it 'off road', i.e. where there is no road at all.
I have friends who do serious off-roading events, and my CR-V is certainly not suitable for that.
Take a tire pump and repair kit.
A winch isn't a bad idea either.
outdoors.stackexchange.com/users/3955/Jon Custer
I have driven my Subaru WRX wagon with M&S tyres on mostly dry logging roads in Northern California.
Ground clearance can be an issue from time to time.
(And one has to resist the urge to go a little faster...)
outdoors.stackexchange.com/users/2270/copper.hat
Could my compact SUV/AWD handle a regular off road track that's suitable for 4x4? Is it a dumb/risky idea?  I understand it would depend on the type and condition of the SUV, the track and the weather. But some general information from someone who have tried an all wheel drive on a unpaved mountain 4wd track would be good.
4x4 vs AWD off road
outdoors.stackexchange.com
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outdoors.stackexchange.com/questions/6734
outdoors.stackexchange.com/users/3482/TelKitty
 Drivers of a Honda CR-V AWD, a Hyundai Santa Fe and  Audi Q5 have reported driving on forest roads, off-road and logging roads.  Tires and ground clearance should be considered just as much as the drivetrain of the car.   Whilst various car models can work, ground clearance is an important consideration.
Various models of car can do the job. Ground clearance is a key consideration.