I believe it was rather more than 'moroseness', and more a case of severe depression. Churchill gave the condition the name 'Black Dog', as some people are known to christen cancers or similar afflictions. I believe it helps them to feel more in control of a condition to name it, which makes it a familiar, rather than an alien invader. Apparently Churchill used to build walls to exorcise his particular demons.
A dog is generally seen as a creature that pads along behind its owner, rarely leaving him for long. The verb 'dog' - as in ideas such as 'bad luck dogged him all his life' - suggests the very same idea...that there is, effectively, no lasting escape from it. 'Black' was, presumably the colour applied to it because of the normal associations of that colour with evil, death, misery etc. Thus, Churchill's 'Black Dog' was an evil presence - depression - that rarely left his consciousness.
"Black Dog" is a term used by Churchill but was used before him describing the nature of clinical depression. Sufferers liken periods of depression to a faithful, dark dog who knows its owner like no one else and always eventually returns to its master through no fault of its own.