I doubt they'd experience nausea, but since the sensation of nausea exists for a reason they'd likely suffer some sort of unpleasant sensation in lieu of the urge to regurgitate, probably pain.

Stomach pain, maybe heart burn.
I've heard of horses dying because they are unable to throw up when they really really need to.

In the case of toxicity, don't forget there are other physical symptoms in addition to nausea like light headedness, prickly heat, pain, etc. Many causes of nausea also have secondary symptoms that in humans are overwhelmed by the desire to vomit, sicne it is vomiting that is of a biological priority.

Typically when there is something that would cause stomach upset, it tends to cause nausea, cramping, or otherwise not so pleasant feelings in the belly. Since equines can't throw up, they may feel something akin to nausea, the acids and such still churning like they would in other species, but rather than coming up, it simply boils and causes cramping instead. I would imagine there would also be an overall feeling of being "unwell", with their body protesting something it can't remove, making them weak and headachy or light headed.

I asked  Hoofer and he said,

"Yes. Horses feel nausea, but not in the same way humans do. When a horse swallows something they are not meant to, it will hurt like nothing else. They do not gag or feel like vomiting from anything else other than actual stomach problems. Meaning if they smell something bad, they won't feel nauseous, same if they were on a roller coaster, or if they had the flu, though sickness is might still make their stomach hurt, but not as much as eating something they were not meant to, or eating to much of something they were supposed to. The pain from these though can lead to kicking at their own bellies, withering in pain on the floor (by rolling) or even biting their stomachs hard. Enough to self mutilate themselves. Horses often die of these conditions."

I'm scared of eating right now.

I wonder if my horses should have this attribute. I would probably avoid the issue anyway since I don't like vomiting. But I guess it's more of a behind the scenes thing or like a worldbuilding thing. I might mind what they eat or are fed, and also if/how they feel nauseous since that in itself is also an emotive device..