No, a
shire is a administrative locality, equivalent to a county. Many place names in Great Britain have
shire a the end: Devonshire, Shropshire, Leicestershire, etc., though it's pronounced something like "sheer" or "shuhr" in these names, and not ˈshī(-ə)r as in the land inhabited by
hobbits. Shires are usually rural (much like the
hobbit land) hence the probable reason Shire
horses are so named, i.e. they are farm horses bred for heavy farm work.
en.wikipedia.org
The Shire was a region in Eriador inhabited by Hobbits.
tolkiengateway.net