I would do it slightly differently. I wouldn't ask everything under the sun over the phone but I would only ask the main things to confirm this is a horse worth viewing.
Concentrate on a brief history of the horse so far, i.e. are you talking to the owner, is she a private seller or a dealer, does she also ride the horse, how long has she had it, where was it before, why is she selling?
Then ask her what kind of rider/activities is the horse suitable for. Don't say what kind of rider you are, wait to see if what they say matches what you want. E.g. if you want a bombproof, first time owner hack, and they say the horse is a straightforward first competition horse, then you know it's not for you.
If all goes well then concentrate on suitability for the activities you want to do, e.g. does it hack? In a snaffle? Alone? In company? In traffic? In open spaces? Does it buck/rear/nap/take off?
In this weather confirm that there are suitable facilities for trying the horse. Never get on a horse the owner refuses to ride!
If all that sounds suitable arrange a time to see. I don't want to write this in capitals so as not to sound rude, but please, please, please take your instructor with you. Firstly she knows you and can assess the suitability of the horse for you. Secondly you can now ask a million questions and you have a witness to the answers from the owner (which you do not have on the phone).
A final thought...can you afford to wait a couple of months before you look for horses. This is an awful time of the year, you don't want to have to get used to a new horse which cannot be turned out or ridden due to the snow and most private owners who are not in any hurry to sell would wait till spring anyway to get the best buyer possible.