Hi Steve,
I had a look at 'Inns of Salisbury' by Roland Graham Gordon. 4 large files of handwritten info.
Unfortunately, his info on The Black Horse only goes up to 1843. His info starts in 1620, when a William Gold was proprietor. Apparently the pub was also known as The Star and Garter for part of its history. To quote from Gordon "1775 The Star and Garter changed to the Black Horse again by George Webb the proprietor. It had stabling for 50 horses and was the starting place for several coaches. "
I also looked in the local directories. Unfortunately, your ancestor didn't choose to be included in Kelly's, which the library has a good collection of.
Langmead and Evan's Directory of Salisbury 1897 - 8, has under 'Inns': Black Horse, Winchester Street, A Biss, Proprietor. On another page, under the alphabetical listings, it has him as 'A Bist'.
The next mention I can find of the pub is in Brown's Directory for 1912. Black Horse, Winchester Street, proprietor A J Gould. The street listing in the same publication shows that the Black Horse, no 18 is on the south side of Winchester Street, on the corner of Brown Street.
The next directory that the library has is for 1925, and this shows no 18 is occupied by Courtney & son, Furniture Dealers.
Attached is a photo of the building today. I'm not sure if the present building dates back to 1620, but it certainly would have been there in 1905 when your ancestor was born. It is now a hairdressers. The photo isn't great as I took it on my phone. I will take another next time I have my camera with me.
If I come across any more info about the pub I will let you know.