I realize the deer would leave as soon as people approach, but the thought of bouncing onto one of those antler points is scary!
I heard recently that some does grow antlers, so I just googled the subject- FOI
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Researchers have noted that females can have a testosterone surge caused by a hormone imbalance, first pregnancy, tumors, or degenerative conditions of the ovaries or adrenal glands. This single surge can cause the growth of antlers in velvet.
Indeed, researchers estimate one in every 1,000 to 6,000 white-tailed females produces antlers. In Pennsylvania, researchers reported one antlered doe per 3,500 antlered deer. A 1985 study in Alberta, Canada, documented that eight of 517 adult does had antlers (about 1 in 64). The reasons for the high number of antlered females in this region: perhaps because every harvested deer was examined, or there may be a genetic predisposition for female antler growth.
http://www.dnr.state.mn.us/volunteer/mayjun04/fndoes.html