i very much enjoy depictions of oromë with animal traits. i think that is a very cool design choice. oromë is my favourite vala and i always love to see art of him. HOWEVER... i would like to provide a perspective i rarely see acknowledged: that oromë is a god who symbolises man's stewardship over the natural world. depictions of him as a very human figure, with all the trappings of civilisation, make a lot more sense to me, considering his role.
oromë's association with animals is all about domestication. he rides a horse, he keeps trained hounds, and he even has cattle. the hunter-god identity could be animalistic; obviously animals hunt. but oromë hunts with weapons, and trains animals to serve him. therefore he has dominion over beasts, rather than being himself beastlike. this dominion is peaceful, not abusive or controlling or unnatural. domestication is seen as good and natural.
on the wilderness as his domain: oromë is called 'the lord of forests', and loves trees, and the lay of leithian calls him 'the forest-god'. but he doesn't live in the forest! he rules over the forests, but he lives in a house; the book of lost tales says it's in the city of valmar (a city can be seen as the opposite of the wilderness). it's full of spears and bows and knives and hunting trophies: all signs of civilisation.
most interesting maybe is the living trees that grow inside. this blends oromë's house into a mixture of the forest and a structure: peaceful cohabitation of nature and civilisation.
the women oromë is associated with also have this theme of peaceful harmony between the wild and civilisation. nessa his sister runs in the forests with deer, but returns to valimar to dance on lawns (lawns that oromë himself 'culled' from his forest glades- hmm!) vána his wife tends to gardens, and picks flowers; we could see this as the feminine version of dominion over nature. oromë is the master of animals and tames them to his will, while vána turns wild flora into cultivated gardens.
so when i think of oromë, i think of furs, leathers, and arrows, not teeth, claws, and antlers. he symbolises a belief that mankind (using this word as a catch-all for non-divine beings) should live in peaceful dominion over the natural world, so he must be man-shaped. hunting is part of that dominion, even though it is associated with death and predation.
after all, oromë's role as huntsman only becomes threatening when morgoth lies and tells the elves that the dark rider will hunt and eat them, not the animals that are his sanctioned prey. and what prey is celegorm hunting when huan, hound of oromë, leaves him for good?