Why is tall grass good for your horse 

Yes it should be dormant - the light levels in February are low to keep it dormant. The only thing to consider is any large change in horse's diet - if it is eating little grass at the moment, to eating more grass (if it's green, that is), give her some stalky rough hay to balance her forage with more fibre. If your field of extra grass is rather brown/yellow, and thus fully dormant, than there is no worry as it's like feeding your horse hay. As for the horse being fat, not sure if you have rug on it when it's out. Keep it without the rug and it'll use its body fat to keep itself warm, thus by spring it'll be leaner. Even in wet weather, horses can cope well, and use their fat to keep themselves warm - which is essentially what getting them fat in summer was evolutionary for, so they can go through lean, wet, cold winter.