We're Spanish drivers, used to nice sunny roads, I expect it would be difficult but doable, but I would like to ask for some things you have to be extra careful which we may not be aware of.
I have driven around Iceland in winter in a small hire car with studded tyres. I would recommend hiring a small SUV with differential lock, if not full blow 4wd.
With this setup, it is fine for slush and I only experienced minor fish tailing which was easily controlled. It meant we could not pass on any road that had not be cleared after a big dump of snow.
Driving at night in rural areas with horizontal snow is very disorientating, especially on elevated roads, as you cannot see anything but the snow lit by your headlights a few metres in front.
Think fog also obscured trucks with lights on, crawling along slowly, until we were only metres behind.
While I was there was a double fatality when two tourists tried to cross a single lane bridge at the same time.
Be careful, defensive and conservative and hire a suitable vehicle, and you should be fine.
My friend and I drove around the ring road in early March 2016.
A lot of the ring road was fine, but even then there was a bit of snow around. Weather is very unpredictable in winter, so there is no guarantee you won't have to drive on a road with snow and ice, even on the ring road. The snow ploughs do their best, but they aren't perfect. We did have to drive in quite heavy snow west of Akureyri, and then again around near Gullfoss
I would definitely recommend not using a 2WD sedan if you're going in winter, even on the ring road.