I meant no criticism of your quote – indeed, I thank you for it. It’s just that when researching a question like this, sometimes it’s useful to find a cite for the cite.
The attribution of the basics of the quote to Guizot appears first in a quotation dictionary by W. Gurney Benham, published in 1948. Benham also asserted that *“Clemenceau adapted this saying, substituting ‘socialiste’ for 'republicain.”’ *
John Adams, the President, quoted in *Thomas Jefferson, Journal, Jan. 1799 *said
So, the Adams quote is verifiable. Guizot, at age 12 in 1799, perhaps had not spoken this sentiment as yet.
All of this is courtesy of The Yale Book of Quotations (2006)by Fred Shapiro. This is the most accurately researched of all quotation dictionaries.
Note that the Adams quote stays in the same mode as the others. Not a distinction between liberal and conservative, but a distinction between youthful radicalism* - the problems of the world are so severe that they must be solved now and by any means necessary - and older repudiation of radicalism. You don’t have to be conservative to think that an extreme or violent solution is not the answer or that the world is more complex than simple black/white solutions can accommodate.
*For Adams, “democrat” was a dirty word, for it referred to the politics of the anti-federalists, which he thought extreme, radical, and dangerous.
Hey! I just find 'em. It’s up to you to interpret them. And you do damned fine work. 
Here also the quotation usually speaks of communists, rarely socialists. Sometimes the point is emphasized by using instead of any specific political ideology just the word radical or idealist. At least this popular form comes probably from French politics. It seems using it towards liberals is a recent American invention.
Some of these attributions are interesting. Aristide Briand probably wouldn’t have said the exact words (well, translated words, that is) that are attributed to him in that one link, as at forty he was in fact one of the most important socialist leaders. However Briand is indeed a good example of youthful radicalism turned moderation: in his youth he was close to anarchists and radical socialists, then followed syndicalism, but in his thirties became an independent socialist and progressed to become a successful prime minister and Nobel peace prize laureate. So I guess Briand’s political career would be very much like what the quotation means: idealism with a heart at twenty, rationalism with a head at forty.
Wikiquote is a very problemous source for stuff like this. Take for example the George Bernard Shaw quote: article history shows it was added without any source or explanation by an anonymous user with no edit history. So how can we know that user didn’t just invent the quote themselves? It’s not that Shaw couldn’t have said it, but even if he did, it would have been just a parody of the other, already famous, quote.
As for whether Winston Churchill said something like this, why not check what the Churchill Centre has to say? In the page “quotes falsely attributed to him” it says:
So those American right-wingers who insist WC said this once again show their poor knowledge of history, as he indeed was a young Conservative, a middle-aged Liberal and finally an old Conservative, while his wife Clementine remained Liberal. Man with no heart and no brain, that Winston. Not to mention that Liberals and Conservatives are British parties and at least in Churchill’s time did not resemble what is commonly though to be liberal or conservative ideology in today’s United States, or here in Europe where liberalism is a right-wing ideology. Finally, Winston Churchill apparently did not think that his own political views would have changed during the years, in his view it was the parties that changed, which seemingly justified his inter-party moves.
Shaw did actually say something akin to the original, in 1933, in a speech at the University of Hong Kong.