My experience is based on 24 days in Iceland and regular monitoring of weather forecasts and road conditions weeks before and after the trip. Conditions may be similar or completely different, when you are travelling, but it gives you an idea.
All highland roads right through the middle of the island are closed! The ring road is the way to go!
In the South, the Golden Circle and up the east coast to Höfn, driving is realitivly easy. There are nearly no mountain passes and the ring road follows most of the times the coastline. We had snow and lots of wind, but driving is easy, the roads are maintained and cleared of snow. Any car with winter tyres will do, a 4WD is not necessary, especially if you can rest a couple of hours, if the weather turns really bad.
The North is a very different story!
North of Reykjavik towards Akuryeri and especially further on to Myvatn, Egilstadir and Höfn you will have lots of mountain passes, steep climbs, nearly no villages and we had lots of snow with new snow every day. The road authority tries to keep the mountain passes open from Reykjavik to Akuryeri and Myvatn, but sometimes some or all passes on the way have been closed for a couple of hours or during the night. The roads, even the ring road are full of snow, sometimes icy for many kilometers.
The large stretch between Myvatn and Egilstadir was closed nearly half of the time, we just slipped through. As soon as you have wind and a bit of snow, it is very likely that this part is closed down, sometimes for several days in a row! In the north the roads climbs to more than 500m elevation several times, which translates to 2500-3000 m altitude in central europe.
For 100km the road was one big patch of pure ice! Look at the pictures, this was daily reality.
If you have a 4WD with studded tyres (spikes), no problem, you just drive a bit more carefull. I would not even think of going there without spikes!