I would find it pretty impossible to comment sensibly on a horse unless I had seen it move, and you get a better picture as well if you can see a horse on different surfaces.
What's sometimes interesting for owners is when I then trot the horse for them - often, they haven't seen their horses trot in a straight line on a hard surface before although if they long rein or lunge, they will have seen their horses trot a circle on a surface.
It can come as a surprise for them to see that stride length in a sound horse changes, depending on the surface the horse is trotting on, whether it is on a circle or not, etc - but it shouldn't really be unexpected.
After all, there is a reason for running dressage competitions on arenas, rather than roads - more extravagant strides. There is also a reason why dressage tests ask for extension on the longest straight lines - across the diagonal or down the long side - rather than on a circle.
Its the same with people - runners on hard surfaces take shorter strides than those on shock-absorbing surfaces (trainers can skew this, as the body is fooled into thinking that its running on a soft surface even on roads). Runners cornering shorten up too.
The biomechanical reason for the shorter stride is to reduce impact stresses on joints and soft tissue, so its actually a very sensible thing to do on a concussive surface or when turning. If you watch a group of horses trotting along a road, most will have a shorter stride (shod or barefoot) than they do when they trot on grass - watch them cross to another surface or go in a straight line and you will see stride length increase.