Well see this horses tail it kinda looks like that it doesn't look fake. Not saying the other two pics the horses don't have fake tails bc I thought they probably were I'm just talking about the straightness At the bottom of the tail
I french braid my mare's tail and always keep it in a tailbag. It grows full, thick and fast. Make sure when you end your braid, to go as far down as you can. It will cause breakage if you rubberband it too high
If you need it straight for a show or something, wash, condition and blow dry with a big paddle brush to straighten. You could also use a flat iron (for hair) on a low setting, but it will take a while. Both of these will dry the hair shaft out though, so don't do it often.