Hi Pam,
The only surname HORTON in my ancestors date back to the early 1700s and are not from Lincolnshire. I had a look on the International Genealogy Index (Church of JC Latter Day Saints) website and found the following results from the 1881 British census: Joseph HORTON born Wigston, Leicester approx. 1839, wife Elizabeth born approx. 1865 at Plumstead, Kent, and children Elizabeth (b.1865), Samuel (1871). Catherine (1872) & Isaac (1879). Is this your family? I also found a Robert HORTON b. abt. 1818 at Aylesby in Lincoln (a labourer) married to Elizabeth b. abt. 1817 at Clixby, Lincoln. But can't find where this Robert & Elizabeth had a son Joseph. This probably confuses more than helps.
Cheers,
Allan