Yes, the Nazis were socialists

See 80 Years Later, Are We Still on ‘The Road to Serfdom’? Hayek saw in 1944 that the loss of economic freedom often leads to the denial of other freedoms by Rainer Zitelmann. Excerpts:

"Socialists in those days avoided describing Hitler’s movement and system as “National Socialism” to deny the intellectual affinity between socialism and Nazism. Today, we know—although Hayek couldn’t have known at the time—that Hitler developed a growing admiration for the Soviet Union’s planned economic system.

In 1942 Hitler defended the Soviet planned economy to his inner circle: “One has to have unqualified respect for Stalin. In his way, the guy is quite a genius . . . and his economic planning is so all-encompassing that it is only exceeded by our own Four-Year Plan. I have no doubts whatsoever that there have been no unemployed in the U.S.S.R., as opposed to capitalist countries such as the U.S.A.”

In July 1941, Hitler said: “A sensible employment of the powers of a nation can only be achieved with a planned economy from above.” And: “As far as the planning of the economy is concerned, we are still very much at the beginning and I imagine it will be something wonderfully nice to build up an encompassing German and European economic order.” Statements like these confirm Hayek’s basic thesis." 

"In a speech in May 1937, Hitler described this philosophy: “I tell German industry for example, ‘You have to produce such and such now.’ I then return to this in the Four-Year Plan. If German industry were to answer me, ‘We are not able to,’ then I would say to it, ‘Fine, then I will take that over myself, but it must be done.’ But if industry tells me, ‘We will do that,’ then I am very glad that I do not need to take that on.”"