Is carbon pricing really a conservative idea?

I seem to have read many times recently that "carbon pricing is originally a conservative idea". Just a few examples here, here, here and here. 

Interestingly, both Right-Wingers/Conservatives/Republicans and Left-Wingers/Liberals/Democrats seem to claim this, the Left presumably in an attempt to sell a tax that is unpopular in most conservative jurisdictions, and the Right presumably in an attempt to take some credit for a policy that seems more and more inevitable. (Incidentally, "carbon pricing" is the preferred label these days, on the grounds that "carbon tax" is an automatic turn-off for all conservatives.)

A carbon tax doesn't seem particularly conservative to me, though, and I have struggled to find any good proof of the claim. One article suggests that the idea originally came from right-of-centre economists like William F. Buckley Jr. and Milton Friedman, although the evidence seems dubious and tangential to me. Another article notes that Canada's first carbon tax was brought in in 2008 by the British Columbia Liberals, "the equivalent of a conservative administration in most parts of the country", but this is not to say that the BC Liberals espoused small-c conservative policies, just that BC politics is so far to the left of most of the country that the Liberals are as right-wing as the province goes.

Given that there is pretty much consensus across the board that carbon pricing is the best, easiest and most efficient method of cutting our greenhouse gas emissions, then maybe the best way of looking at it, as this article concludes, is that carbon pricing is neither conservative nor liberal in itself, just smart.