I've seen posts on Facebook about being aware of a disease that deer are carrying which may make their meat consumption harmful. Is there any such disease in our New Hampshire White tail deer population?

If you are referring to the stories about CWD, currently there are no confirmed cases of any deer carrying the diease in NH

Not as of yet but here is a recent article http://amp.wmur.com/article/concern-grows-after-disease-deadly-to-deer-moose-confirmed-in-quebec/23506758 . Also, there is more information on the Fish and Game website https://wildlife.state.nh.us/wildlife/cwd/