Deer has a symbolic relation with Lord Buddha. Deer are a direct reference to the Buddha's first teaching in the Deer Park, Sarnath (Varanasi), also called Dharmachakra Parivartan.
The suggestion is that so wondrous was the Buddha's appearance and peaceful his presence that even the animals came to listen his teachings.
Especially in the Bhutanese tradition, a monastery, which holds the Kangyur and Tengyur collections of texts, would have this symbol of deer on both sides of the Dharma-wheel on the roof.
Depiction of Deer Dharma Charka is also seen in many monasteries in Bhutan, Tibet and some Indian states.
So my deer friends always have a soft heart to the deer and never ever think of hunting and eating it.
Eating deer's meat is directly hurting Buddha.