I am not an equal nutritionist, nor a vet, but this is a generalized list of things I've learned to see based on the last three decades of working with many unhealthy horses.
I start with an overall zoomed-out perspective. Watching the horse and how they stand when in a calm mental and emotional state can give us a lot of insight as to what they are physically feeling. If they are consistent in postures such as specific odd/compensating leg positions that they seem to repeat when in a standing position, it often reflects pain issues.
Noticing a "pointing" with a front hoof (trying to alleviate pain) can reflect the consequences of an inappropriate diet and a variety of lameness or diseases.
Feeling each hoof for heat can reflect inflammation.
When I look at the horse overall I'm noticing things like the length/texture/curl of their coat relative to the season, their age, and breed. I'm looking at the shine, which is not reflected based on how clean the horse is, but if the horse is producing healthy oils.
I'm looking at their feet, healthy growth, rings, or other visual damage on the outside are obvious markers for changes in feed and diet.
I'm looking at their overall awareness of the world around them as far as how sensitive they are or perhaps shut down. Many quiet horses behave in a seemingly compliant manner because they are often in a painful state.
I'm watching for tail movement and position in response to their environment or activities occurring around them; too many people ignore how much the tail can tell us. Short, fast, dramatic swishing and response to being physically touched can be a very strong paint indicator of gut issues.
I like to start at one end of the horse and work my way along their bodies so that nothing is missed.
I'm noticing their breathing, many horses have developed allergies to environmental factors and you will hear literal breathing issues when they are at rest. I will also do a stress test restricting their air, dramatic dry coughing, discharge of phlegm or partially chewed feed can indicate problems.
Running my hands along the outside of their jaw where the upper and lower teeth meet can often trigger a dramatic response in the horse if there are dental issues which then are affecting how they are chewing and processing feed and perhaps depriving them of nutrients despite them being fed quality feed.
Opening their jaw and smelling their breath. So many horses have rancid-smelling breath reflecting an imbalance in gut acids. Many older horses I meet have dental issues so their diet consists of processed feeds and senior grains; I find all too often the stench of their breath reflects fermenting food in their gut from the high sugar content.
I'm watching for when and if they pass manure, and the position in which they hold their body as they do so. Inspecting the texture of the manure, inspecting for sand, etc. can tell us a lot about their gut health.
If you have the opportunity to watch the horse drink if there is a dramatic gulping and very large quantities of water consumed can often indicate kidney issues.
Being able to watch the horse eat both any supplements and grain, noticing if there are dramatic or odd chewing behaviors, and watching for feed falling out of his mouth, can indicate an inability to break down and process food, which can lead to things like choke and nutritional deficiencies.
I'm looking at the horse's eye; if fatty tissue or a puffiness below the lower lid is present that can indicate IR and gut issues. The color of the inner lid can indicate blood health issues.
Looking at the neck along the side of the mane might have fat pockets when there are digestive issues, sugar sensitivities, et cetera. The more obvious "floppy" or cresty mane that is flipped over is a pretty severe case leading to many potential unwanted health issues such as laminitis.
I also tend to see fat pockets in front of the scapula when horses are not digesting their food well.
An enlarged barrel is common when horses are carrying worms or other parasites. So many folks believe their horse is plenty fat, without realizing it's actually a health issue.
Noticing if there is a "ridge" where it seems the spine is protruding upward, usually about 6- 8" in length, behind the rear of the saddle, can indicate nutritional deficiencies and red blood cell issues.
Along the rump but especially down the back of the hamstring are common locations of fat pockets in horses, especially ones that are older and have had years of imbalanced health.
I'm sure there's more I haven't thought about at the moment but these are the basics that I look at. I hope this list helps you to be able to better assess your horse.