Nightmare Moon: Pretty standard doe with armor here. I gave her antlers because I thought it made her look more royal and god-like. A few female deer actually have antlers (but mostly it's a genetic fluke. Only Caribou females have antlers as the norm), so I'll just roll with it. Deer don't have manes either, but NMM just wouldn't be NMM without the cloud of stars she trails.
Chrissie: It was difficult combining cervine and insect, but after I gave her multi-branched antlers, I thought of the Shishigami from Princess Mononoke, and went with making her more like the Asian Giant Hornet (my thought process is all over the place). Antlers don't usually grow like this, but when they do it looks pretty awesome. The massive antlers work to give her a sort of crown from which her hair falls like a veil.
Sombra: Not much to say here. Instead of regular antlers, I have him single branch, curved antlers like a Gazelle (which, like antlers on does, is possible in many species). One is broken, however, to give a sense of the many battles he's been in.
Discord: The most fun to work on. Since Discord already has several deer-like properties, I decided to make him resemble a deer's predator instead. He walks on all fours, with a body more bulky like a lion, but silent and graceful like a wolf. It also explains the creepy predator look he's got going on. After I had that figured out, I just went wild stylizing everything and replaced his deer antler with that of a moose because reasons.
Fun fact: I was going to nix the fangs on everyone originally, but then I found out some deer actually have them. Specifically the Chinese Water Deer and the Muntjac (one of which I shall own someday).
[from the artist's dA]