Horses should have access to hay all the time.  This is why it is so important to access hay which has a lower nutritional composition, with lower palatability  so that they can learn to self-regulate.

We are omnivores and require a routine of feast and fast, not continual browsing.  This is why we get anticipatory pleasure from our mealtimes.  It is a mistake to imagine that this is normal for horses.  A good reaction to you re-filling their hay feeder would be indifference. It is important that horses are allowed enough hay to be permitted to sift through and leave anything which their palate tells them will not benefit them.

Gradual changes

It is very important to remember that the microbial population in a horse’s stomach is specific to its current diet, this is why you should always introduce new feed gradually, so that new microbial populations have time to develop. and this is just as true with new batches of hay. 

Soaking

With especially vulnerable horses, for example laminitics with pedal bone rotation, or particularly sensitive horses,  it is always wise to soak new hay until they are more comfortable (though it is not necessarily the best thing for horses with ulcers).  But in the long run, one of the aims of the Tested Hay Register is to access hay which does not require wasteful and time-consuming soaking.