Victorian Surname DictionariesThe Patronymica Britannica  provides the following information:
"HOAR. HOARE. Doubtless from A-Sax. hár, hoary, grey; applied to a person having a grey or hoary head. The Common medieval form is Le Hore."An Etymological Dictionary of Family and Christian Names  provides further details:
"Hoare. White, hoar, grey."More detailed information can be found in the Dictionary of English and Welsh Surnames :
"Hore. Hoar, white, grey. Horr, Local a ravine.
"Hoar, Hoare, Hore. - Nick. 'the hoar,' i.e. the white, the greyish white; probably from complexion of the hair; cf, Fairfax, Grey, White, Black.
'Ae olde men and hore
That help-lees ben of strengthe.'
Piers plowman , 1682-3
Very common in the Hundred Rolls , as for instance:
Adam le Hore, co. Derby, 1273. A.
John le Horre, co. Norf., ibid.
Alicia la Hore, co. Oxf., ibid.
Richard le Hore, co. Soms., 1 Edw. III: Kirby's Quest, p. 84. London, 3, 55, 6; New York, 5, 8, 4."
Many old publications can now be found online at a variety of websites. For example a fully digitised copy of "Some Account of the Early History and Genealogy of the Families of Hore and Hoare" is available at the Internet Archive. This was particularly interesting for me as the document identified that in the Domesday Book a village (modern day Ower) was known as "Hore". I am currently a long way from tracing my Hampshire Hoare family back to the village of Hore in 1086 however it is certainly motivating.
|Entry for Hore in the Domesday Book|
(image kindly made available by Professor J.J.N. Palmer. Image may be reused under a Creative Commons BY-SA licence - please credit Professor J.J.N. Palmer and George Slater.)
If you have Hoares (or any of its variants - Hoar, Hore, Horre, Horr, Hoor or Hor) in your family history in Hampshire or Sussex then I would be delighted to hear from you.
 Mark Anthony Lower MA FSA (1860) Patronymica Britannica A Dictionary of Family Names of the United Kingdom, John Russell Smith, London. Page 159.
 William Arthur MA (1857) Etymological Dictionary of Family and Christian Names. With an Essay, on their Derivation and Import. Sheldon Blakeman & Co. New York. Pages 160 & 163.
 Charles Wareing Bardsley MA (1901) Dictionary of English and Welsh Surnames with Special American Instances. Henry Frowde. London. Page 387.
 The Hundred Rolls are a census of England and parts of what is now Wales taken in the late thirteenth century. They are named for the hundreds by which most returns were recorded.