1) Speed is the last thing you need.
I have jumped massive ditches (over 12ft wide) on a 14hh pony from trot. You do not need speed and horses much prefer to be working out the problem. I am never surprised when I see people coming far too fast at a ditch, the horse slams then brakes on . All my horses are introduced to ditches from walk. Its really stress free, they are given a soft rein, legs on and the rider stays in the middle of the horse with their position. They are never turned away from the problem and you keep asking.
2) Its disconcerting but if the horse drops its head at a ditch this is a good sign!
It means the horse is having a really good look at the problem and they are thinking about it. Keep the rein soft and let them look, but make sure you maintain a strong upright position with your leg on. Just do not let them step back. You might need to hold onto a neck strap as sometimes the jump is not that comfortable.
3) If they have frozen and are ignoring your leg, take them away from the ditch and trot them around and get them off the leg again. Given them a tap with the whip to sharpen them up. Once going forwards again walk up to the ditch and ask again. Some small sideways movement is fine but they should not be allowed to shoot backwards. If they resist, make them move their shoulders and keep moving them forwards and around.
4) We used to school all our horses on the lunge with large ditches with water in. If you are worried about the jump your horse might throw, lunge or lead first to help them. It is much better to take the time and do it this way than to give in, make yourself worried or sock them in the mouth.
5) Practice makes a more confident horse – you should keep coming round in walk or trot until the horse feels really confident about them. Make sure you jump the ditch in both directions as its amazing what coming in a different direction will do to the horse! When popping quietly go and jump a few other jumps and then come back just to check the ditch is still confident but remember to pop back into walk or trot. You will know when your horse is confident because there is no drama and they are not over jumping.
6) At an event always take your time at a ditch. I tend to trot a green horse at them because you have plenty of time to sort the problem out if they start backing off. Be positive and if you have done your homework they should be confident.
I would agree that when first introducing a horse to a ditch it should be from walk. In terms of choice of ditch to first use it would either be a super narrow one that can be stepped over or a very wide one (but not deep) that can be walked through at an angle.
The horse has to learn that there isn’t a monster at the bottom and by giving chance for them to look and work out the question in front of them they are far more likely to think rationally and therefore just pop over.
I will always when first introducing ditches have a ditch proof horse to act as a nanny who will either quietly walk/pop over a small narrow one or walk through the wider one depending on options. The nanny horse may only need go over once ahead of the baby but can easily save a lot of time by giving the baby confidence and showing it what to do.
If opting for a wide ditch at an angle first to be walked through you should always always have tackled steps both up and down first. If you haven’t you can’t expect the horse to understand the prospect of stepping down then up in quick succession. The problem with a wide ditch as a starting point is then encouraging them to jump over rather than step through although when approaching straight they will unlikely make the mistake more than once of trying to step through but personally I would prefer after stepping through to move to a smaller ditch which is obvious should be stepped/jumped over not through.
Ditches on the whole are rider frighteners and when introduced correctly and calmly should not cause competition issues.