In the way that political scientists and even the public thinks of "war", the Cod Wars were clearly not wars. There were no battle deaths nor even attempts to physically harm individuals from the other side. The Icelanders tried to stop the British from fishing in the contested waters, while the British tried to continue fishing by evading capture or preventing the Icelanders from sabotaging their nets.

The First, Second and Third Cod Wars more accurately fit the term "militarized interstate dispute" but even the usage of the term is controversial. The dispute of 1952-1956 could arguably also be referred to as an MID but it would be more problematic since the confrontations/clashes were between the Icelandic Coastguard and British trawlers (not the British Navy).

One Icelandic historian thinks of the Cod Wars as ten disputes going back to the early 15th century. Others think of the Cod Wars as four disputes, with the first starting in 1952. More commonly, the Cod Wars are seen as three disputes, which excludes the 1952-1956 dispute.

It's really sort of a semantics question, you can say both are true depending on how you define the terms. No formal state of war existed between the United Kingdom and Iceland, but there were numerous actions of violence (chief among them ramming and warning shots, but even less severe tactics like forcibly cutting nets set by trawlers). The main actions were conducted by the Icelandic Coast Guard and British Royal Navy, two armed services that were definitely in conflict with each other.

The three periods of conflict occurred at different points of time, which could be used to define the Cod Wars as a series of conflicts. On the other hand, their ultimately common underlying factor, the asserted fishing rights of Iceland and alleged overfishing by non-Icelandic (read: British) trawlers, could be used as argument towards considering the Cod Wars a continuous "war".

So...yes.