We went on a 1-week trip in April 2014 (aligned with school Spring Break), when Icelandair first served DIA in Denver. We rented a 4x4 Chevy SUV from Hertz, for driving the Golden Circle and also a daytrip onto the Snaefullsness Peninsula.
The Westman Islands to the south were inaccessible, but would be a priority on a future trip later in the year, partially for seeing puffins. Maybe March/April access is available now??
We took a 2-day private guided trip from Reykjavik to the Jokulsarlon glacier lagoon, staying out there, before returning to Reykjavik. It included a glacier climb, and we brought our own ice axes from home. Our guide was moving to Denmark later in the year, and I don’t believe that company is still in business. There anre still others, though.
We got a promotional lodging deal with Icelandair when they were introducing their new Denver flight service, so we stayed in Reykjavik every night except the one by Jokulsarlon.
We took a “Warm Nights, Cool Lights” tour one night, which involved a bus from our Reykjavik hotel out to the Fontana baths for hot springs soaking and saunas, dinner, and potential Northern Lights viewing. The baths were fantastic, but overcast skies prevented seeing any Aurora. Refunds weren’t part of the deal.
For driving, while you undoubtedly already get your share of tricky winter driving conditions, especially if you venture up by Monument Hill, Iceland has some particular hazards. Super high winds can occur without warning, and digital highway signs show sustained wind speeds, along with gust speeds. Be prepared to get blown sideways, when the conditions exist. Also, black ice is a real danger. We witnessed a VW coming towards us go airborne, shortly before sundown. My husband managed to get stopped on the non-obvious black ice, while I called 112 (Iceland’s 911). One passenger who was in the VW died. After the road got reopened by the authorities, we got back to our hotel hours later, after the hotel’s restaurant had closed. It could’ve been worse.
We never had deep snow (or any snow on the road, really) while visiting, but the roads were still hazardous.
March might be different than our April experience, so hopefully you’ll get additional information from others. Have a fabulous (but safe) trip!