Icelanders are evangelic-lutheran which means that they are quite liberal about their religion, have a lot of churches in towns, cities and the countryside but don’t go to mass unless special occasions. Christmas is a special occasion in Iceland.
Christmas is taken seriously in Iceland. The families get time off, all the companies close for Christmas and the families concentrate on celebrating. They go to church on Christmas Eve at 6pm, midnight and or the day after. This is how it has been until very recently. Nowadays it is possible to find a few grocery stores and restaurants in the centre of Reykjavik that are open. Nothing is open in the suburbs.
Christmas is family celebrations in Iceland. For most families the main celebrations take place on Christmas Eve. They go to church at 6pm on Christmas Eve, 11pm or midnight and or (possibly again) the day after, have dinner at 7pm, open presents and stay at home or visit relatives. On December 25th the families meet again, have coffee and cakes or eat dinner together. On December 26th some of the families might get together again.
Iceland is quiet during Christmas. No shops are open, no restaurants or cafés to speak of but some tour guides take their guests on tours, e.g. me. Christmas is mainly a time for resting.
If you are going to Christmas mass here in Iceland then I recommend checking when the English-speaking mass takes place unless you want to attend an Icelandic-speaking one. Please notice that there might be a reason to go early to church to get a seat.