Good question. Firstly the Welsh open access maps aren't line at the mo so I'm going by the latest OS explorer map and my professional nounce, and the following is general advice and may vary between locations
Virtually the entire FC estate was dedicated as Open Access under section 16 of the Crow Act 2000. This gives the public a legally protected free access to 'explore' at will anywhere on that land. There are some exempt areas such as within a certain distance from dwellings, and the owner/occupier can restrict access for certain reasons such as land management, nature conservation or public safety for 28 days per year. MTBing would not qualify for a restriction, unless it was for an organised event and fall within the 28 days available. All they can do is advise that MTBs may be present, but they can't legally stop the hapless walking on the trail in most cases.
On open access land the owner/occupier enjoys greatly reduced liability to the user - the legislation assumes that you understand the risks associated with remote open country and should you fall off a cliff then it's simply your own fault. However AFAIK this has not been tested in the court's yet and how this relates to permissive use by MTB on the same land I'd hate to hazard a guess at. But having been aware of other countryside court actions they tend to be taken on a case by case basis as the conditions are different for each event so it;'s difficult to set a precedent.
Bottom line is unless the land is specifically closed off (ie restricted access) for the purpose of MTBing then you should expect to encounter other uses who may have more legal rights to be there than you
Rights of way are a different matter entirely, and is not covered by the reduced liability mentioned above.
Incidentally some MTB routes at Coed y Brenin run along unsurfaced unclassified county roads, so there's a good change of a horse or vehicles being encountered.
FC cycle code -
http://www.mbwales.com/media/viewfile.aspx?filepath=1_20080520101237_e_@@_cyclecode.pdf&filetype=4