The first time you go to view the horse watch and ask for the person showing you horse to do the following with him.

The second time, if there is one, watch again for signs of the following and you handle the horse do all the same tasks.

It you need a third time ask for it and be prepared to buy or put down a deposit (maybe not refundable).

Is the horse healthy looking?
 Alert, interested, no unusual discharge from nose or eyes, no swellings or  excessive cuts.

Is the horse easy to catch, halter.

If the horse is at pasture, ask to see it caught.
 Stalled: does the horse com forward eagerly or cower in the back?

Ask to see the horse lead.
 Does he follow well, turn easily, stop, stand, tie or cross tie?
 No signs of limping, dragging feet, tripping.
 Does he step out well with his back feet coming up underneath him?
 Ask to see him lead at the trot as well as the walk.
 Is he pushy or try to drag the handler?

Ask to see the horse groomed, saddled bridled.
 When grooming, does he seem to have any ouchy or tender places?
 Any places he wants people to avoid?
 Does he pick up his feet well to have them cleaned out?
 Does he offer to kick or bite when grooming or saddling?
 Does he shy away from the saddle or pad?
 Does he stand or dance around continuously when bridling?
 Does he take the bit well or throw his head up and require a lot of coaxing?

When being mounted:
 Does the horse stand or walk while the rider is still getting on?

When being lounged:
 Does the horse shy, trip, drag the handler?

While being ridden:
 Does the horse move out freely, respond well to cues or does he back, act up, rear,  shy excessively, not move off the rail, toss his head, wring his tail, not slow down  unless the rider is really pulling, refuse to walk, not turn well?

After being ridden:
 Does the horse show excessive stress, sweating, blowing, coughing, or limping?