Sadly, Walt Disney passed away in Dec. 1966, so he was only around for a little more than 11 years of Park operations. Major refurbishments were not required during his lifetime, however many new upgrades, rides and attractions were added and they must surely have required construction walls (the Matterhorn opened in 1959 and that was a very big project).
Today those walls are a fact of life at a 51 year old park. There's no way around it.
Please visit my Big Thunder/Disney Inspired Model Railroad
While major refurbs didn't happen during Walt's time, there were clean ups needed. But back then, the park was fully closed on Mondays and Tuesdays (except during summer, Christmas, and 2 weeks at Easter break.) Much of what needed repairing could be done then.
If you see a cute yellow lab puppy with a yellow cape, WAVE! It might be us! (Or it may be someone else that lurks here!) Thank you for asking before you pet! Next trip, Dec 22-Jan 3rd.
Walt shut the park down just to clean it up back then. But they still need to have multi-month closures 51 years later. And since rides like the Matterhorn are so old, it tends to wear down much quicker than say a ride like California Screamin'.
An in-refurbishment closure is much better than a permanent closure and a tarped building is much better than a crapped out facade.
Disneyland was in constant contruction during Walt's time. Mine Train ride though Nature's Wonderland got improved several times with major new features. The Matterhorn and Subs were built. Tomorrowland got rebuilt a few times. New Orleans Square got built and opened during Walt's time. That made Frontierland into a huge mess, and Walt mentioned it on one program. Of course, something amazing was always waiting when those walls came down.