Let me try to go in order here:
Yes, there appears to be a softer source edging the actor's (and horse's) legs. I didn't comment on this before because the whole scene has a magenta tint to it and I figured that edge was created off the background lights. It could be one huge light source scraping the entire frame, in which case some heavy diffusion was probably used as well; but I think there were probably multiple smaller units. Notice the separation in the horse's legs. His back legs are colored and the front are not.
The blue you see on the other side of the horse is coming from a completely different source. My first thought was that maybe they used some negative fill by stretching a large solid on the left side of the frame, and they may have, but that blue color is coming from somewhere. Whatever it is it's a soft source with some sort of dark blue/violet colored gel. Could be a kino, could be an LED, or it could be a heavily diffused fresnel. It could be a million things. All we really need to know is that it's a soft source hitting from frame left with some colored gel and diffusion.
I think it's important as a cinematographer to know the exact look you are going for WHILE SHOOTING. Sure you can tweak things in a post a bit but the idea is to get it as close to the desired look as you can while in production. If anything I'll take some contrast and saturation off on camera and adjust levels accordingly while grading; but color should be as close as you can get always.
As for differences in light fixtures:
Fresnel - A fresnel light is defined by the lens, which is the same as they use in lighthouses. It's what comes into your head when you think classic film light. They are balanced at 3200K and allow you to focus the light by using the spot/flood knob located on the back of the fixture which brings the globe closer to of further away from the lens.
HMI - Hydrargyrum medium-arc iodide lights are very similar to fresnels except they are daylight balanced (5600K). There is a spot/flood mechanism as well (on most fixtures) but you can also change the lenses if you want the light to spread wider or to be more narrow.
PAR - Parabolic aluminized reflector lights are classic stage lights you might see overhead at a theater. They're essentially long cylinders which emit intense oval pools of light with unfocused edges. You can also switch globes in these fixtures depending on how wide or narrow you want the source to be.
To clarify a few things you said before, any of these lights has the power to create deep shadows. It just depends on how close your subject is to the light, what they're standing against (open space, wall, floor), and if you're diffusing light at all. It's not so much that HMIs are better for outdoor use it's that they are daylight balanced so it's easier to match color temperature when shooting outside. They're also great for shooting through windows when you want to mimic daylight during an interior scene. Lastly PARs can have higher output but they also can not. It all depends on the wattage of the fixture. A 750w PAR will not have a higher output than a 1.2kw HMI or a 1kw tungsten fresnel. The major difference is that the light produced by PARs is much harder with more definitive cuts. This is because there is nothing between the globe and the subject and no lens to focus the light.
I really hope all of this helped you get a better understanding of how light works and the differences between fixtures.