Not at all. I always start a horse trotting over fences and trotting out. As they develop balance and engagement over the fence I start trotting in and cantering out. Only after they are able to do that well do I canter in and canter out. Even my best jumpers will be asked to trot in and trot out on occasion.
A horse does not need impulsion to jump bigger fences as much as they need balance and engagement of the haunch. I will walk a horse up to a fence that is 3' and jump it from a walk. It is no problem if the horse knows how to use his haunch.
No amount of impulsion will replace engagement. A fast moving horse may just as easily be heavy on its forehand making any jump ackward.
just to clarify - I believe you are confusing impulsion with speed. Impulsion is engagement of the hind end and propelling the horse fro behind, so essentially one and the same. With regards to horse movement, fast does NOT = forward and I think that is where your confusion lies.
For a horse to be able to jump from a walk, he needs impulsion in the form of engagement of the hind end and back muscles.
To the OP I agree with the comments quoted (save for the clarification on impulsion). Forward is important - forward comes from impulsion. Fast is NOT important, as fast does NOT necessarily include balance or impulsion. Trotting in and trotting out is a great way to teach a green horse to jump without rushing with a focus on a steady rhythm and pace. If the horse ONLY knows to trot in and canter out, effectively you're training the horse that after landing, they need to speed up - and can you imagine how disastrous that could be over a full course with a semi-green horse?
Here's an article I wrote that may help, including the USEF definition of impulsion as it relates to engagement of the hind end: Understanding Impulsion, Suspension, and Action in the Gaits
Often you hear people talk about a horse's suspension, impulsion, and action, something you hear most in the Dressage rings, but you will hear with regards to other disciplines as well. Hunters are known for having "flat knees" and saddleseat and carriage horses have "high action", while dressage horses are known for having "great suspension", but just what does this mean?
First, let's look at the difference between suspension and action. Suspension comes from impulsion. Action specifically refers to the action in the joint that occurs during flexion and contraction of the muscles around that joint. So a horse with more action in their hocks simply flexes the muscles and joint in a more pronounced way (this also can be impacted by limb angles and conformation) than a horse with less action. Suspension is the time in which the horse is suspended from the ground during any particular gait. Suspension will occur more naturally in horses who are better built to carry themselves conformationally meaning that they also have more natural impulsion or self carriage.
Next, let's define impulsion. Impulsion is the ability of the horse to propel with energy from the hind end, specifically defined in the USEF Rule book as: "the transmission of an eager and energetic, yet controlled propulsive energy generated from the hindquarters into the athletic movement of the horse. Its ultimate expression can be shown only through the horse’s soft and swinging back to be guided by a gentle contact with the rider’s hand."
So how do suspension, impulsion, and action all relate when discussing movement of a horse? Quality movement must have impulsion. A horse moving with impulsion will have more suspension in their gaits than a horse moving without impulsion. And a horse must have good joint action in order to be able to be able to move with impulsion and thus suspension. However good joint action and excessive high action is entirely different and not always desirable. So how do you tell the difference?
A horse with high action may appear at a glance to have more suspension but to be sure you need to look at actual movement. If the horse is not carrying themselves and moving with impulsion, then the actual time where the horse is physically suspended from the ground will be less than a horse with true impulsion. This can create the illusion that suspension and action are directly related, when in reality, a horse can have less joint action, but better self carriage and impulsion and actually stay suspended from the ground longer because they are propelling themselves forward rather than up. Remember that less exaggerated joint flexion coupled with more hind end power (impulsion) will still equal suspension.
Now that the difference between impulsion, suspension, and action is clear, we can better understand the "flat kneed" movement of a hunter and the "high action" movement of a saddleseat horse, and the suspended movement of a dressage horse.
With a typical hunter, judges look for conformation and soundness coupled with an even pace that would be comfortable to ride on the hunt field for an extended amount of time. This is where the "flat knee" expression comes in. A horse with less knee action and a free flowing shoulder will have a stride that is long and smooth making it easy to sit. When this horse moves with impulsion, the result is a long forward stride with quiet joint action. Think of the difference in riding a horse with sweeping movement as opposed to a non-gaited horse with a lot of joint action - the horse with the sweeping movement will be easier to sit to for a longer amount of time.
When it comes to saddleseat horses, you tend to see judges looking for that high stepping joint action referred to as animation, coupled with good impulsion and energy. Over-exaggeration of joint action is undesirable, however a naturally more active horse will be considered more animated, which is a criteria for which horses are judged. Animated movement which includes more noticeable joint flexion coupled with impulsion and suspension is most often see at the "Park" gaits, which as per the USEF are considered highly collected and animated. In this case, both impulsion and action are needed, collectively creating suspension that shows off the animated movement of the horse.
Finally, how does this relate to the dressage horse? In dressage, impulsion is looked for at every level in every gait. The more collected the horse in their movements, the more action they will need to have in their joints to perform that movement with quality while maintaining impulsion. For example, a horse performing an extended trot will use their impulsion to propel them forward in the gait, with more forward suspension and less upward suspension as they cover more ground. On the other hand, a horse performing a piaffe will need significantly more joint flexion in order to be able to maintain impulsion while staying in the same place, causing the impulsion to push them upwards rather than forwards. A horse overflexing their hocks at an extended trot is equally as undesirable as a horse performing the paiffe with sub-par hock flexion. In dressage, a horse with impulsion, action, and suspension will place well, however impulsion is always most important and the action of the joints must match the movement being performed.
The key to quality gaits in any riding horse is impulsion, regardless of discipline. The amount and type of suspension and action that goes with that impulsion will vary by discipline and the movement being performed.