There are over 700 species of Eucalyptus (and related genera that look
similar to Eucalyptus and may be called that) that are adapted to
tropical, temperate, desert and alpine regions of Australia. Some are
quite frost tolerant, especially when mature, but by no means all.
Most occur in areas that would be equivalent to USDA zones 8-10 but the
alpine areas that some are native to are zone 7 so if you had one suited
for that it MIGHT overwinter in 6b. The rest are likely to do very
What species is it?