Using the FreeBMD site
http://freebmd.rootsweb.com/cgi/search.plEnter the details and then press search and you will find the reference for Wincanton. Click on the underlined 'Wincanton' and it will bring up another page which says 'The district Wincanton spans the boundaries of the counties of Dorset and Somerset; information about it can be found
here: click on 'here' and you will find a list showing all the parishes within the district showing the registers are divided between South Somerset and Poole. Click on the relevant one for Wincanton [South Somerset] and it will give you these details:
The Register Office, Maltravers House, Petters Way, Yeovil, BA20 1SP.
Tel: 01935 411230. Fax: 01935 413993.
E-mail: yeovilro[at]somerset.gov.uk
However, the GRO reference is of no use to a local register office and, unless they have now indexed the marriages, it is unlikely they can afford to check registers of all the churches/chapels within that huge registration district for the 13 weeks that make up the March quarter of 1860 to locate said marriage. It is a mammoth task!
I suggest you make initial enquiries via email and, if they cannot assist, you will need to obtain a copy from GRO to establish where the marriage was conducted. If in a parish church for which the Somerset Record Office holds the church register, you could minimize costs by obtaining a photocopy from SRO which would give original signatures [if any]. I went through a similar process some years ago to obtain original signatures for a marriage in Staffordshire in the 1890s in order to confirm the identity of a witness.
Update:
You could suggest a likely parish [perhaps North Cadbury?] in your initial enquiry to the registrar.
