It seems that he went to great lengths to conceal it. How effective was this?
In exchange for unprecedented access to FDR as a political figure, the media willingly avoided publicizing the president's fairly obvious disability. Conspiracy is a dirty word, but plainly stated the executive office, secret service, and media conspired to avoid projecting images of his disability to a wide audience. It wasn't seen as a huge deal largely because their wasn't an appetite to see it as a huge scandal in the US at that time.
This said, many people in the United States were well aware FDR had contracted polio as a young man and since polio was fairly common at the time, they were often well aware of the effects of the disease.
Here is an article from 2013 contextualizing how rare footage of FDR in a wheelchair is to find - http://historynewsnetwork.org/article/152604