Yes, we do. We keep a record of what he's done in terms of schooling/hacking, etc. during the week . . . including what he found difficult, breakthroughs we had. We also include things that may have happened on the farm to upset him - the stallions being on the yard, someone taking Rog out of the field, Frey coming in before him. Any changes of feed or changes in his intake of food/hay/haylage/water and the state of his stable (if unusual) are recorded. Lastly, we record what happens when he goes out to competitions/clinics . . . right down to what he was like to travel, whether he ate or drank, whether he stood nicely to be tacked up, etc.
We find it helps us spot patterns we might not have noticed, and our dressage trainer really uses it too. Doesn't take much time to fill in. I keep it on Excel so that I can graph a particular activity to see if we're doing less or more of it than we have in the past. As an example, when we moved to current yard, Z also changed jobs so was available to ride more often which meant Kal spent much less time on the lunge/in the Pessoa and more time on the walker (which we didn't have at previous yard) . . . that and no longer feeding him some of his forage from the floor resulted in a change in shape (and not for the good) . . . being able to look back at what we had been doing differently (without evening thinking about it), helped us work out why his topline had changed AND change our management/riding routine to reverse the process.
P