The Red Cow, Harpenden
I couldn't find a lot but I understand that the public library at Harpenden has a very reasonable collection of books relating to Harpenden, and may also have microfilms of the censuses, so you best bet would be to visit it. The Harpenden Local History Society may also be able to help.
Basically all I found was a reference in Hertfordshire Inns & Public Houses saying that the earliest know reference was to William Attwood being the licensee in 1851, and identifies some later landlords. This suggested a check in the published transcript of the 1851 census for Harpenden (again almost certainly in your local library). I found that William Attwood (43, born Wheathampstead) was living at "Cold Harbour" and was described as an agricultural labourer and beer house keeper. With him were his wife Elizabeth, two children - Amos and George, and a niece Fanny Hawkins.
In fact many small beer houses were run as an addition to an ordinary job, and such establishments were normally not listed by name in the trades directories, etc., so can be difficult to research. It could well be worth your while checking to see if William Attwood is listed in the 1841 census - as if he was at the same address he may have been operating a beer house there, even if this is not explicitly listed in the census.
If you can add to the information given above tell me.