I lease a 17 hand 11 year old OTTB gelding named Beretta. He's a supercute horse and is like a giant dog. It's winter, and most of the time I don't get to ride by myself because since we only have one indoor ring and the weather can make the other outdoor rings unsable. When I do get the indoor ring all to myself, though, I like to keep in mind a few things. First, I know it's easy to throw away your position when there's not someone there to constantly tell you to "keep your lower leg still" or "shoulders back" or "close your fingers on the reins" I'm sure most of you have heard these critiques quite often, as I know I certainly have. When riding by yourself though, it can be easy to forget about posture. I have a tendency to not keep my shoulder back enough and to sit a little too in front of the vertical. To fix this, and so I don't have to contstanly remind myself, I sometimes grab a crop, and stick it between my back and through my elbows so it forces my shoulders to be back.
Another thing that tends to be common when riding by yourself is when your warming up, you just kind of go around and around in a posting trot or canter. When your riding by yourself these things tend to slip your mind, but you really want to remember them. Changing up your warm up is a great way to keep you and your horse thinking and fit. Try a sitting trot, no stirrups trot, collecting and extending, figure eights, circles, serpentines, spirals, groud poles, everything! Same at the canter. Beretta tends to be more excited to the left, so today I worked over ground poles. There was one at the far end of the ring in the middle of the short side by the gate, and two in the middle on each long sides. We trotted over them, and each time he didn't nick a rail, I praised him. We tried to maintain a consitent pace and we tried this in both directions and at the trot and canter. We also tried some flying lead changes- crossing through the middle and asking for the change at X, and a flying lead change, coming at a jump from an angle-which encourages the horse to pick up the correct lead over the jump.
When riding by yourself try to keep a mental check list of exercises to do with your horse. Keep in mind what areas are your horses and your own strengths and weaknesses. I'm sure you'll have a great ride next time you're with just you and your horse!