With all our faults we are pretty damn welcoming to foreigners. While customs officers won´t exactly hug you on arrival they will neither give many too hard a time.
Iceland is part of the Schengen agreement meaning people within a Schengen country can travel without difficulty to Iceland and do not need any special visas. There are also other agreements in place for other nationalities but the main thing here is to take care your passport is valid for longer than a few months.
The overall picture is found at the Foreign ministry to which you can also write if in doubt about anything.