I am not sure what you mean by "regular insurance" but you can by medical and mortality insurance. There are companies taht specialize in equines. If you are looking for a particular company do a internet seacrh for equine insurance or ask your vet for some.
The last time I called for a lease it wasn't an issue to purchase it for a year, and then cancel once the contract was up. Keep in mind you'll have to pay for the entire year up front, and then will be reimbursed for the rest after canceling.
The ONLY problem you may/may not have, is how the policy is paid out in the worst case scenario. You have to ensure that the they will pay the major medical out to you if you have to pay for it up front, and the mortality insurance out to the owner. So it's just a matter of how you set the policy up. The other thing you have to make sure is that you have the ability to cancel the policy and that you don't need the owner's sign off - this was one of the hardest things to find when I tried to insure a lease. Two companies I called would refuse to cancel the policy without the owner's sign off - which, is great if you trust the owner 100%, but if you have any doubts in your mind, you could end up paying for an insurance policy for a horse you don't actually own.
Let me know how it turns out for you and if you find an insurance company that will work in your specific situation.