In the case of my husband's grandfather, we found a muster roll online about the WWI members n a website created about his unit by the Vietnam veterans. I think it's safe to say that it's less likely that you will find an equivalent roster for someone who served in the 1790s, but never say never. There's no telling what you might be able to find about the Somersetshire Militia until you look, so ask instead "how might I find more information?". It's not wrong to consider that fewer records survive from that period than they do for the modern day, but don't let that consideration block you from performing your search.
Since the links for all the archives are changing, I'll write out the path I took; if the individual links fail, perhaps this will leave enough clues that someone following after can find a similar path. If individual pages move or change, older versions may be available via the Wayback Machine. Starting with a Google Search for "Somerset Militia" --
Museums and Archives
The website of the Army Museums Ogilby Trust offers a sub-page on Ancestor Research which says:
It is recommended that once an individual's regiment or corps has
been identified a researcher's initial approach should be to the
appropriate regimental or corps museum, details of which may be
obtained from the museum pages.
Their Somerset Military Museum page refers the reader to the museums page on the Somerset County Council Website; a link in the sidebar goes to the Somerset Miltary Museum page, which advises that the Museum's own website is still being written and will appear in future. This page has contact information for the curator of the museum and for the Somerset Archive and Record Office at the Somerset Heritage Centre.
The County Council's site also has subpages about the Somerset Heritage Centre and the Archives, and a link to the Archive's own site: Somerset Archives and Local Studies. The front page has a caution about the online catalog and a link to work-arounds on the Catalogues and Indexes Page, plus a link to the Library Catalog.
The left-hand sidebar has a link to research guides, with Army Records (PDF) near the top at the list, and A Guide to Our Indexes (PDF) near the bottom.
For a general list of other useful sources for army research see the website of the Somerset Light Infantry Archive.
Books found on via the Library Catalog can be searched for in libraries near you, via WorldCat; older titles might be available in their entirety on The Internet Archive or on Google Books.
- a search for 'su:England, Somerset Military history.' at WorldCat turns up documents published in 1642! so there's no telling what might be added in future.
- Brit-Gen has a sub-forum Military-Army under Occupations; there are some threads in the archive about the Somerset Militia from a slightly later time period.
- Wikipedia has no article, but a search for Somerset Militia yields hits for articles that mention the militia.
One caution: a search on Google Books also found hits for a "Somerset Militia" in the US Army, so a search in this particular time period will not be easy. Adding "England" to the search won't necessarily screen out the American unit because the books will mention England as an adversary.