jumping is up to you, dressage you should but don't have to again with the dressage faze of eventing, for the xc and sjing up to you and showind depends on what horse you have anything but a native should be plaited.
Plaits are traditionally done on the horse's right side (off side).
This is so that the rider can view the horse's conformation before mounting from the left.
And we mount from the left, because, as right handed people, our sword scabbard lies on our left side. By mounting from the left, I am sure you have found, your sword scabbard doesn't get stuck, or inadvertently stab your horse on the way over.
S
In showing (non native) and dressage it always makes your look much smarter and shows you have put effort in. Also in showing classes if the judge is torn between placing a plaited pony and non plaited pony 1st, they usually choose the plaited pony. Showjumping looks smart but i would always try to consider the comfort of the pony 1st as tight plaits arnt comfortable for them so may affect their preformance. ODE's i would plait up for the dressage if non native pony then take them out for the xc and sj. Hope this gives you a slight idea
Always plait on the off side (right) with an uneven number of plaits on the neck and with the forelock you get an even number.
The yard I trained at wouldn't let you off the place for a competition without being plaited - and sewn! So from habit if I'm competing I plait. Only time I don't is for the annual foal show where plaiting is forbidden! Yeah!!!
If you sew the plaits, you can also be clever about how they sit on the neck to flatter it for showing.
You can leave the start of the plait slightly less tight to allow the mane to bulk up a little to disguse a poor base to the neck.
Not that I'm saying that about your horse, btw, it's just a trick.