Without seeing a picture it almost sounds like you are describing is a ground cover rose or like you say a climber. You may want to go out to HelpMeFind web site and you may be able to identify it. As far as special care for mini roses, there is none. I treat mine like any other of my roses.

You may also want to post your question with a picture on the Rose Gallery forum.

With minature roses ,just cut down the amount of fertilizer that you would use on the big roses.

I received 4 miniture rose bushes when my Father recently past away. They have bloomed all summer, so I know he was taking care of them because I do not have a green thumb at all. I took off the dead blooms every two days, I had lots of roses that took their place. They are in a very large unmovable pot in my rock garden, how do I winterize them for the long cold and windy Northern Alberta Winter. If I cut them back and them wrap them with a burlap material, will they survive. Your help would be greatly appreciated.