I was just there a month ago from March 30 - April 5. We drove the south coast highway all the way to Jokulskarlon. Stunning scenery!
We had every kind of weather and road condition you can imagine! Long swaths of ice on the road, rain, fog, beautiful sun, and WIND. The wind there was different than wind I've driven in before...it's almost like narrow rivers of wind gusting horizontally across the road from the inland mountains towards the ocean. We had two strategies for dealing with this. Get behind a car or tour bus, wait to see when it gets jolted by a gust of wind, hold onto the steering wheel, and keep it on the road. We also could watch the snow blowing in small ribbons across the road wherever the wind was gusting. Like the previous poster said, the road here is unforgiving. We saw quite a few cars that had either been blown off the road or had gone off the side for whatever reason. They had been taped by the police for pickup later. Just stay aware and take your time.
The biggest thing that scared me were the other tourist drivers who didn't seem to be paying attention to what they were doing on the narrow roads. Several times I had to flash my lights and lay on the horn to alert drivers coming towards me who were drifting over the center line. The one-way bridges were fine for us...we never had an issue with people not taking their turn.
You really do need to make sure you are covered for gravel / sand - we were hit by many rocks on the highway that were thrown up by tour buses, other cars, and trucks. With the wind we experienced I can imagine that, if you are in the wrong place at the wrong time, your car would be completely sandblasted! You will drive through large fields of pulverized lava and I'm sure they become tiny projectiles in windy conditions.
I have a Chase Sapphire Preferred credit card that covers me for any and all damage so that's the card I used to rent our car. We rented through Fox and they had a sign on the counter that claimed NO insurance covers gravel, sand, undercarriage, etc., damage...they want to scare you into buying their extra insurance. We didn't buy it - the guy behind the counter took my card, looked at it and said, "Oh this card. No one with this card ever takes the extra insurance." Just be sure to know what the insurance you already may have through a credit card might cover, or not cover. With some cards, if you take the extra insurance from the rental agency, it negates the insurance you have through your card. Just know before you go!