I had always understood that "whinny" implied a sense of excitement or happiness, & neigh was a more general horsey sound, but various dictionaries have told me thisboth words can be & are often used interchangeably.
Anyway, this all led to a VERY interesting "neigh" & "whinny" discussion with the journalists at work last week. Their conclusion was "hennir" for both or "hennir doucement" for whinny which I found totally lame. Maybe French horses don't make the same sounds as Australian ones ;)
Then there is the "nicker", the "blow", the "snort"...... Ah. That's probably opening a can of worms.

Ha, but I feel I have to say something here, as a horse lover, and working with them.
We have "ébrouement" for snort, some people even say "éternuement" but we have only one verb "hennir" to describe all the sorts of cries the horse can produce, from the low and tender "Voo-voo-voo" sound the mare utters to call her foal to the cry of a defying stallion.