I have a little more complicated feelings about this matter. I think that old horses do indeed become less able to keep weight on. Their systems just don't work as well as they age. And of course, their teeth need work more often.
However, I wouldn't feel too confident that 'he's just getting old' if my older horse was steadily or suddenly losing weight. Old age does not require an animal to look like a hat rack.
For example, this spring we got a poor quality load of hay. In two months, two horses lost both fat and muscle over their toplines and lost covering over their ribs, the older horse more so. The pony looked fine - being a very 'easy keeper' it did not affect him. We got new hay, but didn't see a rapid improvement so started supplementing with a product that supplied more fat and minerals/vitamins. It actually took a few months for them to 'catch up' again.
First, I'd weigh the horse with a weight tape. I weigh my horses about once a month and would get a look to see how much of a downward trend there really is. I'd 'score' the horse (there's a fat scale score that is easy to apply) - I do that about once a month too so I can see if there is a change and how much. I'd try to get a picture if the horse is starting to look odd - in other words, ribs and hips sticking out yet pads of fat over the crest etc. I'd be looking to see if there are ribs showing, and yet pads of fat on the crest, on the rump, or around on the sheath, in other words, something about the appearance not quite adding up, in other words.
I'd make sure his teeth were alright. I'd have the dentist out and have him work on the horse's teeth.
I'd worm the horse and all others on the property, and perhaps review my worming program. It's recommended to alternate wormers and I'd see if I needed to change my program by reviewing it with my vet.
I'd consider that maybe my older horse is showing a problem with my management, that perhaps the younger ones wouldn't show because they're just a little...younger or of a different type - my youngsters might be Morgans, say, and my oldster a Thoroughbred. Maybe I am depending on my pasture too much and due to weather, stocking rates or just the gradual depletion of the pasture over time, I need to make some changes. If dry weather, too many horses, I'd reduce the hours/number of horses on the pasture (stall them more hours a day, say). If the pasture is getting depleted, I'd take the horses off it, fertilize (and perhaps lime, ask ag extension office for testing info and advice), and keep it unused for two weeks or more and let it recover, meanwhile increasing my amounts of hay to compensate.
Maybe I'm not giving enough hay. The old timer might need more time to eat, without competing with the others. Sometimes older horses get pushed away from the hay more. I'd also look at my hay. Maybe that last delivery of hay wasn't so good. Maybe the horse is not cleaning it up - perhaps there's a lot of waste to it. I'd try switching (gradually) over to a better hay, and/or feed more hay, give the older guy a place to eat where there isn't any competition, etc.
If the oldster is not getting any grain or fatty supplements, he may need it. I'd try something like Grow N Win or a senior feed that is extruded (pellets or whole grain might not get digested or chewed as well). If I was feeding grain, I'd look over what type. What am I feeding? Maybe it's not calorie dense enough. A flax product or simply topping his grain with a little corn oil might be all he needs. Maybe it's a whole grain, and the old timer needs a rolled grain as he doesn't chew as well as he once did.
I'd work on those things and start weighing the horse once a week with the weight tape. I'd keep a record of the weights, so I wasn't relying on my memory. And if I was still seeing my oldster losing weight after making some changes around the barn that should be making an improvement, I would indeed start to be concerned. Old horses often get illnesses of old age, and a great many of them cause noticeable weight loss. I'd first test for very obvious and inexpensively tested things, such as getting a fecal count on the old timer.
Most people's 'eye' is a little off. Some endurance folks or eventers tend to equate 'thin' with 'fit' and might be less concerned if an oldster drops weight(there is, indeed, a difference between how a lean, fit, muscled up horse looks and how an underfed horse looks). Others might love all their horses to be 'hog fat' and be super alarmed if an old timer starts to look thin - certain types of riding tend to prefer a horse that is fatter, and certain breeds tend to be sort of roly poly.
To top it off, some people are novice owners, and the day to day changes in a horse's energy level and behavior might alarm them. A person might have his horse be very lazy and disinterested one day, see a little weight change, and become overly alarmed. Or a novice might want to have his horse really heavy, fat and a weight loss down to a more normal, healthy level might alarm him. The weighing and the scoring are what takes out the personal bias and makes things more even-handed.
Too, keep in mind that the owner sees the horse every single day. A horse can lose a surprising amount of weight and the person who sees him every day, may not see it at all, because he sees what amounts to 'no change' each day, it happens gradually over time. But again, the weighing and scoring and keeping a record is what prevents these things from throwing one's eye off.
If an old horse showed a SUDDEN weight loss, I'd be at the vet's door - immediately. What's 'sudden'? Well, a dehydrated animal or one whose internal organs aren't working right, can 'draw down' very, very fast, and the coat can suddenly look dry and 'hidebound', with muscle mass decreasing and fat covering rapidly disappearing. Suddenly finding that the girth has to go up a few notches or that the horse's neck, shoulders and rump look different from the saddle or cart, is a lot of weight loss. And there might be a change in weight of 50 lbs more in less than a few weeks.