I did strip grazing with sheep to keep my fencelines chewed down. I used white electric rope with white tread in posts. I just left the rope strung on the tread ins and moved it as a unit - threading and unthreading the rope was a pain. I used two strands so they couldn't reach over or under - probably would use the top and middle notches for horses - she is probably capable of jumping over it as the tread ins are usually not high but if you have a perimeter fence that isn't a big deal. If you you talk to farmers who use strip grazing for cattle they'll tell you the rule of thumb is put them on the grass when it is at eye height (when the head is down grazing) and move then when it is at nostril height.
If I am reading this right, your horse will be kept in a 10x40 area, correct? I would at least triple that to be 30x120, and even that doesn't have a whole lot of area to move around. 10x40 feet is enough room to jog for a few steps, but nothing more for a horse. Horses are made to move around and run, not be kept in a little pen. Also, you would probably have to move your horse 1-2 times every day. I would fence as many 80x120 areas in as I could, which is a quarter acre. 200x200 feet is roughly an acre.
The OP said that they were going to make the stripes 10 to 40 feet wide not 10 by 40 feet.
I would make them roughly 20 feet wide and as long as possible( or wider if they would be under 100 or so long). Also from the pictures the pasture looks like it wouldn't hurt to mow and other maintance for it. I wouldn't use temporary fencing it would be a pain to move, at least have enough posts you wouldn't have to more them daily (which they would in a 20 by 100 area), if you make seven paddocks just rotate through them for a week, each in a state of mow, rest or in use, harrowing.