Looking for trails that are open in mid-March for a multi-day hike. I believe Laugavegur is closed, and I haven't found much in the way of marked trails.
In March Iceland would still be covered in snow and ice with daily highs of 3*c on the south coast and an average temperature of around 0*c. Most days it snows.
Daily High and Low Temperature in March for Reykjavík, Iceland
You might be able to ski tour if you have the skills to survive in arctic weather, but I highly doubt you'd be able to hike, even on the southern coast.