I ride primarily in the order of tack horses go in (I do my own tackups so horses that go in the same saddle go all in a row, for example), who's in what paddock (can bring two in together rather than making one trip and then going over yon for the next one and then back to the original paddock later), who is jumping today (so that I can clutter the ring with jumps for the shortest possible time by doing those ones all back to back) and, for some of the ones that are a little wild yet and might upset other horses and riders, "Is the ring clear?"
Personality/size/training level of the horse makes no difference.
I tend to go with greenest or most difficult first. That way I'm fresh, on my A-game and ready for whatever they can dish out. And I always try to save the best (my personal favorite - usually one of my own) for last. Kind of like horsie dessert!
All other things being equal I ride the ones getting the school/ naughtiest/ greenest first before the ones that are just hacking. Which is usually when the telephone company/ oil delivery/ farm equipment magically manages to show up no matter how much I have tried to avoid them. If no one is particularly challenging I do it however is most convenient which can be any number of the the ways meupatdoes describes.
I just read a scientific article that found the more decisions we make in a day, the more poor choices and decisions are. Can you eliminate all the easy decisions - tack, schedule, what you need to eat, plans with friends, training plan - by making those decisions the day before or as a schedule. Then, you will use all your decisions on the most important - what outcome do you want from the time you spend with each horse? Business leaders were using this to have better work outcomes. Maybe the philosophy can help trainers better manage the zillion decisions needed for training horses. Good luck!
Not a pro, but I have 4 horses I ride. I go one of two ways, the best for last, as I'm least likely to skip riding my favorite, or the one who needs work the most goes first...which is usually still leaving the best for last!
I often will order them based on saddle they go in, but currently, only two are in the same saddle.
I'm not a pro, but I do a sortof working student deal during the summer season when my barn is super busy.
I do my personal horse first because she is the easiest and I like to start out the day in a relatively good mood. Also, if I need to drop one because I run out of time, she can't be dropped. She needs to get out every day.
Which leads me to my organization:
Horses get out in the order of who needs to be ridden most. So if I had 5, it would go
1. My mare
2. Horse who needs a heavy flat school
3. Horse who needs a good flat school
4. Horse who needs to get out and work
5. Horse who needs to cruise around
This is so I have my most difficult rides when I have the most energy. It is difficult to ride the energy-suckers at the end of the day, especially since I tack-ride-wash-grain each one myself. Also, if something comes up (a wild farrier has appeared to disrupt your schedule!) the horse who gets a vacation day is one who won't be super wild because of it the next day.