Know WHO you are dealing with.  Is this person someone whom you are happy to be associated with?  Reputation can be everything.  Consider checking with the registry to see if they have any issues or complaints about that individual.

Find out how they care for their horses.  What is the vaccination and worming schedule?
What worming products do they use?  What do they vaccinate for?

Ask about the horse's training.  Does the horse ride or drive?  What process did the trainer use?  Ask to speak directly with the trainer. 
Are they willing to learn or stubborn?  What level are they at?
Have they shown the horse?  How did the horse cope with the stress of showing?
How did they adjust to the new situation in their life?  How do they interact with other horses or people? 

Ask to talk to their veterinarian. Can they give you a copy of the horse's records?  What procedures has the horse had in the past?  Injuries?  X-Rays?  Surgeries?  Has the veterinarian preformed a soundness & lameness exam  on the horse?
NOTE:  You will need the horse's current owner to contact the veterinarian to give permission for them to discuss the horse with you.

Pre-purchase exam, who is going to pay for this?  Consider x-rays for soundness problems.  Lameness exam is suggested.
What about reproductive issues?  If you are purchasing an animal for breeding, get a reproductive evaluation done by an experienced equine veterinarian.
    MARE: What is her reproductive history?  How does the mare behave during heat & breeding?  With a foal at side?
    How many tries each year before she'll catch?  What is her foaling history?  Any troubles in the past?
    How many foals has she had?  Any concerns with health or conformation of the foals?  How does she care for the foals?
How does she react to people right after foaling?  How about during the first couple of weeks?
    Be sure to include an ultrasound, culture & biopsy on an older broodmare.
    STALLION: Are there any lesions or growths?  Does he appear to be "clean", without drainage or infection?
    Have him collected and checked for semen quality.  How does the stallion handle the breeding situation? 
    How many mares has he covered?  How many foals?  Any health or conformation issues with his foals?

Ask to speak with their farrier.  Are there any hoof issues you should be aware of?
How does the horse stand for farrier work?  Inquire about both trimming AND shoeing.
Do they require special shoes or care?

VERIFY everything that you can.

Use a purchase contract or lease agreement.  Ensure your rights!

Trial period?  Horse returns or refunds?  Deposit?  Refundable or not?  Buy back option?  Right of first refusal?

Retained breeding rights?  Gelding clause?  If the mare is in foal, who gets the foal?  What if she loses the foal before due date?  Breed back or refund percentage (value of the foal)?  What about bred back options or discounts?

Transfer and/or registration costs?  Consider transfer costs for all the registries.  CMHA or AMHA or BOTH!  Consider all the registries the horse is registered with or eligible for registration with.

What about futurity nominations?  Sport horse inspections?  What does each party require the other to do, and WHO is paying for the cost of these items?

Stipulate the new leasee/owner's rights with regards to leasing or selling the horse BEFORE the horse is paid for in full or the end of a lease contract.

Defaulting on payments.  Detail out the payment schedule.  How much time must pass between the last payment and a default of contract?  What notifications and procedures must be given or followed in order to recover a horse who has fallen under a non-payment situation?

Include a clause as to what happens with regards to the payments that were made on the horse.  Will they get a refund of moneys paid?  Will they only get a refund if the horse can be resold?  What if the horse has fallen under bad care?

Insurance!!  Be certain that the horse has been insured for accidental death or injury.  Do they have liability coverage?  Ask to see the policy!  This will assure that the seller is paid should the horse perish after purchase, but before they are paid in full.  Include it in your contract!  Horse MUST be paid for in full, regardless of time or place of death after the contract is signed and/or the horse is delivered.

Horse care AFTER the purchase.
BEFORE DELIVERY:  Who is responsible for the horse's care until it reaches its new home?  Is the new owner responsible for board cost or veterinary care?  What if the animal is injured or dies while under the previous owner's care?  Will the buyer get a refund or option to purchase a different horse?
AFTER DELIVERY:  Be sure to include guidelines for the care of the horse in their new home.  Include a clause in the contract that stipulates what will happen if the horse is found to be in poor care or treatment.  Be sure to include who pays for what if the horse has fallen into bad situation and must be removed and nursed back to health.

If you must repossess a horse, be sure to talk with local authorities before you step foot on the property!  Be ready to provide proof of contract and payments received.  If you must travel across state lines, be sure to have a local veterinarian ready to do a health exam and certification for you.  Locate a place for you and/or the horse to stay within the state for a couple of days to ensure time to attain a Coggins Certificate and Health Certificate.

Who pays for it?  What service to use? REFERENCES for that service!!

Who pays for health certificates, Coggins, etc.?  Are these included in your pre-purchase exam?

Timing of delivery.  Consider the climate in each location.  Think about the travel conditions over the entire route during the time of transport.

Exporting/Importing??  Check out all possible cost factors.  Remember that the horse may be required to spend time in an isolation or quarantine area.  Possibly in both countries.  Be sure to include these costs in your contract, along with who is responsible for which fees.