These horizontal ties are held by two nails on each side...There are four such horizontal ties. I do not have any collar ties at all on top of the roof.
Those nails will not hold much! If strength was necessary, they would have jointed the timber, maybe a butt joint. It looks as if it is only nailed there, rather than jointed - perhaps you could confirm?
The reason I've been so interested in this thread, was that my own roof is of similar construction and layout, but only included one of those horizontal timbers, with a single, well jointed heavier, timber V. Like yours, the horizontal timber was simply nailed in place, with a couple of relatively thin nails. Needing better access to the far end of the space, after thinking about it for a good few weeks, I decided it was simply there to hold things together temporarily, whilst the roof was constructed.
What I ended up doing, was adding a bit of timber at each side down from the horizontal, with a tenon joint, fixed at the bottom to the side of the V. I then added a timber to make a step, at the base of the V. My thinking was, if anything did show evidence of movement, I could simply bolt some timber to rejoin the cut pieces of horizontal, back together. That was 40 years ago, and there has been absolutely no movement.