Certified GKH Gardening Expert
These are called suckers. Most of the time they grow more shrub like than tree like. Beyond this, what you describe is something that can happen to grafted trees. The grated scion (the part above the ground) dies in severe cold. The more hardy rootstock (what the scion was grafted to) survives and since the scion is gone, sends up suckers to try to survive. What I mean to say is that it is unlikely the suckers at the base are the same variety of tree that you originally planted there.