New Year’s Bonfires belong to Iceland's authentic traditions which have been practised there for centuries. For a tourist, it's a perfect occasion to mingle with locals and take a glimpse into local culture and traditions. The bonfires are lit across Reykjavik as well as its neighbouring towns on the New Year's Eve, mostly at 8:30 pm, rarely later at 9 pm. The bonfires are accompanied with songs and dancing which partly helps to beat the cold.
Despite such a friendly atmosphere, you'll still need some warm attire to keep yourselves warm.
Celebrating a New Year the way locals do is an absolutely unique experience not to be missed. Local operators even offer tours specifically for this occasion.
Concerning the fireworks, it's not recommended to bring some to the celebrations of that kind—clearly for safety reasons. Although, people tend to break the rules. If you have prepared fireworks and want badly to fire them out, please do it at a safe distance from the bonfire.