Could a horse-like creature have human-like hands as its forefeet without changing the way it moves?
Short answer: No, sorry.
Long answer: You see, horses are ungulates, meaning they walk on the tip of their digits. This was a process that took a few thousands of years to happen, resulting in the fusion of some digits, as well as hand bones, and loss of the others. Horse hands are quite differently structured than ours and aren't composed of the hooves only. Technically, these are the horse's hands:
Human hands on the other hand, are great for grasping, climbing and holding stuff, but if the way you walk doesn't hint that, it's been a couple thousand years since they've last aided in walking, if at all (nowadays it's assumed we evolved from a primate which didn't knuckle walk). Additionally, walking on all fours using only the tips of your fingers and toes (be careful though) should give you an idea of how much pressure the horse's hooves need to support, and how much the different pressures mattered to reach a forelimb anatomy that looks so different from ours.
So summing up, trying to put human hands on a horse structure and expect it to run is not that different from putting human hands in a bat and expect it to fly (both are cases of limbs being highly specialized to fit a certain purpose, which will not be able to function as intended if such drastic changes occur).
Edit: remember that hooves are much better at absorbing impact and avoiding injuries while running than our hands (see how people who deal with construction work and similar physical tasks tend to naturally develop stronger and more tough-skinned hands to help avoiding injuries and cuts). Additionally, our fingers could get in the way due to not being adapted to bend bend in a direction that'd be opposite to their normal flexing direction. We also need to remember horses don't have quite the range of movement our arms do, as they evolved to move in a 2d plane (left and right), while we came from an ancestor that moved in a 3d plane (left, right, up and down), so even if it could have hands in the place of their phalanxes, I don't think it'd be able to use them as we do (further anatomical changes to allow for such movement would further impact on what makes it such a good runner). If what you need is grasping ability, remember that options such as prehensile tongues, lips and/or noses have been used by other ungulates (giraffes, rhinos and elephants are all ungulates, even if some don't look like so).
Get down in a kneeling position, legs and forearms on the ground. Note that the elbows touch the knees.
Now observe how a cat or dog does it. Same thing — the elbows of the front legs touch the knees of the back leg.
Now, watch a horse do it. The front hooves touch the back knees.
When a cat or dog runs, they put their feet way out in front of their front knees, and they pull forward with their front legs.
A horse extends their 'knee' way out in front and the feet are tucked behind the knees.
When a cat or dog jumps a barrier, they extend their paws first. If their front foot touches the barrier, it is the sole or pads of the foot that makes contact.
When a horse jumps a barrier, it puts its knees way out, and tucks the feet back under the body. If the front foot hits the barrier, it is the top 'shin' that hits the barrier.
Humans, or any animal with front paws or hands, would jump like the dog or cat, front feet first, not like the horse, knee first. It's all about how the front leg joints bend (the joint in the position of the human elbow, although in the horse it isn't really the elbow but the wrist) in the horse vs. the dog or cat. So the method of running and jumping is totally different between the two.