The only ride I know of that goes near Sequoias is Grant Grove (but it is not a day trip, I think they have 1 hour and 2 hour rides). The ride that went near Sequoias in SNP is closed, as it is was too damaging to the ecosystem of the Sequoias (and the Grant Grove ride goes in areas that are already heavily impacted by human feet, so I suppose they figure it's not making much of a difference).
There could be something like this in the Sequoia National Monument, maybe someone knows about something outside the National Park boundary.
The horseback ride from Cedar Grove goes through some beautiful terrain, though, with Jeffrey and Sugar Pines, and meadows. The whole area is beautiful. You can do a day trip there and get into some of the high country (that's the picture that's shown with the horse's ears in the front at the top of the park's horse page):
So I'm thinking you want the Grant Grove ride. It will take you to places that you could access by foot, but it is a beautiful area of Sequoias. Dead Giant Loop has a giant, now-dead tree it in, but the area has plenty of amazing, living Sequoias in it, so I think that's what you want.