I wouldn't call myself an expert but I've taken a class and have read a couple books on trees. The general idea is that when trees are dormant it's less trematic for them to be transplanted. So anytime while they don't have leaves. Winter doesn't work because it's hard to dig--so fall or spring.
Trees are absolutely fascinating. If anyone wants to learn more I'd recommend this book:
The hidden life of Trees
http://www.torontopubliclibrary.ca/detail.jsp?Entt=RDM3462468&R=3462468
After reading this I'm surprised how many trees survive in the city. Especially surrounding by concrete and with so little of the resources that allow them to thrive. Not to mention salt, acidic dog urine, bark damage, and the direct sun and heat.