Leasing can be a great option if you are not ready to purchase your own horse. I have leased several times before and had great experiences. The horse I own now was a horse that I started off leasing and ended up buying. All of the leases I have ever done were "free leases". Meaning that I had use of the horse if I paid the expenses (board, farrier, etc..).
As said before, just be sure that you are clear about what the expectations are in the lease. Make sure you and the owner understand who is responsible for what. If the horses were to need vet care, who is to pay, etc...
A friend of mine ended up leasing her horse to somone I knew and it turned out really bad because the horse became sick and the person leasing the horse did not get the horse the vet care he needed. The horses owner lived out of state and I happened to see the horse daily. I ended up having to intervien and call the owner to let her know what was going on.
A few questions I would ask and would want in writing:
1) Is there a fee to lease the horse and how much is it?
2) Are you going to pay full or partial board? How much is the board? Is the horse to be kept that it's current facility? Is the horse stalled or pasture boarded and does the leasee have the right to move the horse to pasture board if appropriate for that horse?
3) Who is responsible for Vet bills?
4) Who is responsible for farrier bills?
5) What equiptment is provided?
6) Can the leasee take the horse off property for shows, trail riding, etc...?
7) If the horse is injured, who should be notified? Is the horse to see a particular vet? Farrier?
These are just the ones I can think of. Pritty much, just be sure you know what you are getting into before you decide to lease and it can be a great experience. You will find your riding improves and you may get the idea of what it is like to own your own horse, so that one day, when you are ready, you can purchase your own horse knowing what to expect.