In military science, a war is surprisingly loosely defined; most definitions travel along the lines of "violence or the threat of violence (by an organised group) to achieve a political effect". Some definitions put things in, like Keegan's understanding of war as also an act of cultural mobilisation. Some definitions are reductive, like Clausewitz's famous "war is policy by other means" (- he plagiarized this from Scharnhorst).

So if we look at the Cold War - certainly, like /u/MisterMomo says, there were elements of the metaphoric there in the name; after all, it was a "cold" war, not "hot". The two major powers didn't fight each other direct. But by all the military science definitions of war, the Cold War qualifies not just as that, but as actually a war.

The Cold War used violence and the threat of violence to achieve political effects. Directly fought proxy wars by both the USSR and the USA attempted to shore up their own influence at the expense of the competitor. Nuclear missiles and the MAD doctrine used the threat of violence to secure strategic territory against attack. The explicit cultural mobilisation - "freedom, democracy, individualism, the free market", verses "collectivism, communism, the New Soviet Man, central planning" - was done on a grand scale. The Cold War was also a period of government policy enacted through other means; activities occurring within its contexts, such as the Space Race, for example, and the "Star Wars" programme, are campaigns fought against an enemy. You could use any useful definition of war, and find the Cold War fits into it.

As for your question "is it considered to be on the scale of other wars"; that is tricky, and depends on how you're scaling things. Politically? It was on a huge scale. It literally forced almost the entire world to choose a side, and kept them bound to that side for forty or sixty years (depending on when you reckon the Cold War started). Militarily? Still huge in the expenditure of treasure undertaken, and by overall worldwide military size. Casualties? Not many. But casualties actually have nothing to do with war, except for being an unfortunate side effect. This might seem callous, and for that I am sorry, but killing other people is only the medium through which an organisation attempts to break an opponent to their will. So we can't really use that as a measure of scale (although everyone sure as shit wants too). It would be like saying the house you built must be huge because you used the biggest hammer.

Regardless, it depends on what you personally consider to be the thing to be measured, for the scale part of your question.

TL:DR; yes.

It really depends on what you consider as an actual "war." The general consensus, I believe, is that the Cold War is not considered to be a "war" per se, rather the term "war" is used in a metaphorical way rather than a literal way. The Cold War is a term - perhaps dramatically used - to describe a period of tension in the world, particularly between the United States and the Soviet Union. I myself would consider the Cold War in a more ideological way perhaps - communism and the West. The Cold War was an overarching theme, with many ACTUAL wars taking place. As a consequence, I would consider the Cold War to be an epoch rather than a war.