No, being in EEA means EU citizens can _live_ there without working for up to 3 months, but after 3 months they need to be employed. It's the same rule as in the rest of EU countries.
Brits, Americans, and various other citizens can live there for 3 months fine.
For working though EU citizens can just rock up and get a job
"If you are a citizen from a state outside the European Economic Area (EEA), the European Free Trade Association (EFTA), or the Faroe Islands, you must obtain a residence and a work permit before working in Iceland. "
Certain foreign nationals are exempt from obtaining a temporary work permit. This includes citizens from countries within the European Economic Area, countries within the European Free Trade Agreement or from the Faroe Islands."
"EU/EEA citizens do not need a residence and a work permit in Iceland and may stay in Iceland for up to three months without registering and moving domicile to Iceland. The relocation to Iceland is quite simple in terms of bureaucratic related issues for EU/EEA citizens.
EU/EEA citizen staying longer than three months an Icelandic ID number is needed and change of domicile is required."
Which I believe is the same as moving to an EU country. Certainly my parents had to register for things like EKA and some other things when they moved to Greece back in 2001. I suspect moving State in the US is similar (otherwise how would you know to pay state income tax?)
I could work fine in a bar in Greece during the summer without any of that as I was only there for a couple of months, and this was before my rights had been removed.
Compare the process with the UK
"
All non-EU/EEA citizens require a residence- and a work permit in Iceland and need to apply through Iceland Directorate of Immigration (DOI).
....
The Immigration Process
Employment confirmed
Welcome Center contacts the newly recruited employee.
Employee accumulates required documents for immigration purposes and keeps the Welcome Center updated on the process.
Employee sends all the required documents to Iceland, to the Welcome Center.
Welcome Center submits the documents to the Directorate of Immigration and keeps the applicant updated on any developments.
Welcome Center notifies the applicant of the accepted application and the preliminary issued permit.
Employee applies for a D-visa to Iceland at a relevant embassy - if applicable, depends on citizenship.
Welcome meeting upon arrival at the University of Iceland, Welcome Center.
Employee registers formally into Iceland through Directorate of Immigration - appointment and a photoshoot.
Employee undergoes a medical checkup - if applicable, depending on citizenship.
"
But at least Brits get to enjoy those brexit freedoms.
