I don't quite know what to think but goodness me she's moving like she's sedated! Too alert to actually be sedated though.
Any chance of x-rays of her neck? The vet's diagnosis is the first thing I would suspect but I would want x-rays to see the severity.
I had a horse that I suspect had neuro issues but he didn't present like that so I can't really offer my experience... mine fell under saddle but moved normally. Complete change of temperament from submissive wimp in the pasture to nasty nasty bully that was taking big chunks out of the other horses [over a very short period of time]. Until he started taking chunks out of other horses I was looking for a companion home for him... but, with very good reason, nobody wants a companion horse that's a nasty bully.