NO!--They NEVER have touched mine. I have over 50 different species, most species spend the growing season outside in an area of DENSE deer traffic. They don't ever seem to notice them. I also have several hardy ones in the ground (Windmills, Mediterranean fans, some Sabals, and Needles). So these are even uncovered in the winter snows and they never touch them. I have been amazed by this myself. All my non-tropicals are also by necessity highly deer resistant plants (holly, boxwood, herbs like lavender and rosemary, etc.) By the way, I notice they ignore a good many of the tropicals (bananas, BAMBOO, philodendrons, cycads, and ferns among others). Ornamental grasses are also left alone. I can absolute guarantee you--your palms are safe. Would be interested to learn what their secret is! Plant away but I would wait until the SPRING to plant a palm in zone 7--better to get them through a good growing season (you should also protect for the first season or two until really established). Good luck!