You'll probabaly want to avoid physical contact from between the tree and your plant. Even though they are both plants, what is harmless or even benificial to one , may in fact be deadly to another. I am talking bacteria or insects. The insulation of your pot alone will keep it safe enough, though you will have more problems with catapillers and such.
Avoid using sappy evergreens, as the when the heat makes the sap run it can destroy young buds if it drips on them, and most likey whack your potted soil's PH awry.
Avoid fruit trees as they attract lots of birds which may decide for they want a buzz
I have grown sucsesfully in trees before but you must really plan it out . And you need to make sure no one sees you climbling the same tree all summer.