Both.
Critiquing the picture, my first ration is the horse' 'pose', just looks unnatural. It's certainly not a flattering stance, probably exaggerated by the angle. Then the setting itself isn't great. The lighting is rather poor and flat. As Phil mentioned, the red, I don't know cones? Jumps, in the frame are distracting. Background is confused; the tree-line, is neither rendered o provide context nor taken out of focus to emphasis your subject.
This starts to make 'sense' of what's going on.
Immediate reaction to this is "Ah! Looks more natural there! It's the 'rope'" (Been thirty five years since I put a saddle on a horse, so forgive me I have forgotten the technical terms!)
BUT, in the display picture, you have cloned out the rope, which is actually a 'contextual element'. It I adding 'something' to the picture, by way of explaining why the horse is standing the way they are. It isn't just 'clutter' making the photo more confusing or messy... ironically, the red things center left are messy and confusing, and adding nothing to the photo, BUT... you left them 'in'.
And STILL in neither pic is 'noise' particularly noticeable.
Now, presumably at the pixel-peeping resolution you are viewing to clone out the rope it is.....
Which begs a conclusion; you are putting an awful lot of importance on the camera, and expecting that to do so much of the work for you, and then more in post-process, using that to try and make your capture 'better'..... which is all pretty typical newby stuff, BUT what you aren't doing is anywhere near the same level of attention in 'pre-process'.
To which, I would answer, 'nothing'... ho hum.... 'everything'. NOISE is not really 'the' problem, it's your entire 'approach' to taking the photo.
"North South East West check the corners THEN the rest" Look, REALLY look at what you have the viewfinder. If you don't want it in your picture, take it out at source, NOT in editor! Take the time to recognize what is 'contextual' and what is 'incidental' and be more discriminatory of what is adding to the picture, and what is taking away... NOT in the ruddy digi-dark-room, but at source, IN-CAMERA.
From the top then first 'problem' is the situation lighting; this is essentially a 'portrait'. It's not a situation shot, where you are trying to capture an action or situation, where that 'act' is as or more important than the subject, and might have to tolerate and work within the situation without influencing that situation. Its a portrait; ad OK, you cant really ask your horse to look at the camera and say 'cheese' but you CAN pose your subject how you want, and you can set the shot how you would like; no different to taking a portrait of a person.
Think how you would approach taking a photo of your child in their best cloths. You wouldn't just stand in their bedroom doorway, whilst they were watching telly, and expect to get something you would like to stick on the mantelpiece like the school photo's.. so how does the school photo photographer get that 'traditional' portrait?
First thing is that they pay almost NO attention to your child whilst they are about it... they set the 'stage' for the child; they set up a back-ground, they set up lighting, they 'make' the picture, BEFORE they put the child into it, let alone, before they press the shutter button.
Translate that 'approach' to what you are doing... OK, so the local school might be a bit perturbed if you tried setting p a studio set in their hall and then walked a horse in... but, in 'pre-process'; think about the set-up;
IS the field the 'best' setting for your shot? And if it is, what can you do to 'stage set' the scene'?
If you don't like the lead rain in the composition, CAN you remove it from the horse, rather than try and remove it from the photo? Will it stand still, long enough without it?
If you cant get rid; ca you work with it? It causes a lead line the eye will follow; so can you use it in the composition; lead the viewer to another element, a person, or a post, something 'contextual' to the composition, rather than leaving an ambiguity?
Is it the 'best' lead rope to include in shot? Do you have one that is a more 'natural' colour? Or one that is more flamboyant and could be a 'feature' element within the composition? Or do you have some other 'tack' that would do the same job, and either distract Les or add more to the composition?
Those red things? Are they movable? Could you shift them somewhere out of shot? If not, could you 'block' them from the shot? Stick some hay bales in-front, or throw a tarpaulin over them or 'something'. And that is if you have to go that far, and cant exclude them from frame just by shifting position, and standing the horse over to the right a bit, and positioning yourself a little to the left with the camera.
Trees? Neither fish nor foul in your shot, and the confused rendering in the high magnification crop, they are nether sharp focus adding 'context' to the picture, nor out of focus disassociation subject from back-ground drawing viewers attentions to the subject. And it's in that 'confusion' you are seeing the 'noise' you are so worried about exaggerated. IF you had used selective focus to distinctly chuck the far background oof, then that 'nose' would probably be far less noticeable, even at that high magnification. Alternatively, IF you wanted to render them sharp for context, you don't have the light to do it....
Lighting? Why shoot at 4pm, the lights low, ts poor its flat, its not flattering your subject, why not try again in the morning, or early afternoon? If that's not practicable, what could you do with artificial lighting? On camera flash, used for a little fill in, on your subject could do an awful lot to lift the subject from the scene; it would light up the horse, and chuck that back ground into shadow, and give the 'dissociation' selective focus might, as well as increase the contrast and lift the horse out and into prominence, as WELL as sort it the 'confusion' in the back ground AND eliminate 'noise' in it. You don't need to go o far as complicated radio flashes or lighting stacks... but you could...
Its ALL in your control.....
And THAT, is the problem here. You are taking control of the camera; you are taking control of the processing, with big obvious buttons dials and sliders that say "Press Me".. but you are NOT taking control of the PICTURE, which starts in the planning, and the set up ad the COMPOSITION, long, long, LONG before there are any buttons to be pressed or twiddled.
Impractical? Not what you are about? Too much to do for 'one' photo? Begs more questions than it answers, but takes us back to the very beginning... why are you picking up the camera? Why do you want a photo? Whats it for? Who's it for? How is it going to be seen? DO you really need to go 'that far'? Do you WANT to?
It's not an utterly rubbish photo, to start with; but you are paying far too much attention to the wrong 'things' and far to little to the ones that might make a difference, IF that difference really matters.
So Back to the top; "yes" you are expecting too much from your camera, AND I would say your computer; you are putting the onus on them to do 'all' the work, in the instant and after while having no expectation on yourself to do much but pick up the camera and press a button; paying little or no attention to planning or set up, or even what you see in the viewfinder when you do pick up the camera. Which is again typical beginners mistakes, but NOT ones in camera dexterity or control, or post-processing technique. It's fundamental, at source up front 'attitude and approach'. How you THINK (or don't!) about making a photo.
What's needed is a shift in your approach and attitude; you need to stop looking at the camera, and then at the picture. Forget the camera's knobs and dials, forget the computer's buttons and sliders; pay attention to what yo are looking at BEFORE you pick up the camera, and BEFORE you press the shutter button, and take control of the picture BEFORE you make it.