earleb is correct, and I think its worth laying out a bit of how this works.
We do not set policy for any land manager, be it ebikes, horses, what criteria define a 'Blue Square' trail, or how many accessible parking spots there are. For most of Fromme, allowed uses and activities for parks (and trails) are set out in DNV Bylaw 8310, which is adopted by DNV Council. We don't put up trail signs, boundary signs, or use signs (with the exception of TAP signs). We don't get to decide who is allowed on what trails. We are fortunate to be allowed to build and maintain trails, per the standards and guidelines laid out by each individual land manager.
We advocate for mountain biking, mountain bike access, and mountain bike trails, with currently seven (?) different land managers; be that with staff or elected officials. This involves discussions with and about other user groups, be it hikers, runners, streamkeepers, or professional dogwalkers, and understanding that each land manager is unique in their needs, mandate, regulations, policies, and resources. None of those seven give us control over who can be on what trails; we can offer opinions, comments, and thoughts on behalf of our membership and users (advocating), but we can make no decisions on access.
Equestrians are absolutely allowed on many trails on the Shore. The biggest artery on Seymour is named after them.
TL:DR; "Perhaps NSMBA does not have the authority to determine which user groups can and cannot use the trails within their network?" Bingo.
*EDIT: Also, I totally wouldn't advocate for 12 months of sunshine. It wouldn't really be the Shore, I'm terrified of a massive interface fire, I like skiing, and I hate dusty trails. But advocating for sunshine would be as effective as advocating for mountain bike trails can be sometimes.