Was Jesus a Socialist?

There would be no way to know. At the time there were no industries for the government to own in the sense that they do now.

I'm inclined to think that he specifically didn't have political opinions.

Examples would be:

When they tried to trick him into saying that you shouldn't pay taxes and that tithing was more important, to which he replied "give to Rome what is Rome's."

When he turned the trading tables at the temple.

It's fairly clear that he purposefully didn't want to have anything to do with political discussion. So, I doubt he would have any opinions on this.