Option 1: Difficulty traversing
As others have posited, perhaps the land bridge is particularly difficult for nothorses to traverse. Horses are pretty well adapted to open, rolling steppe. It wouldn't actually take that much of a change to make it unlikely for them to make the crossing.
Lack of water, swampy territory, heavy woodland, presence of poisonous plants that they're not adapted to (ragwort in real life is deadly to horses), lack of grazing, too much grazing (one of the issues horses have outside of the steppe is the high sugar content of lush European grass, which causes health issues).
Any of these, perhaps dialled up a bit, would do well to restrict their range.
Option 2: Predation
In addition to the other answers about physical land barriers or poisonous flora, predation could also work.
- Continent B has nothorses.
- Continent A has something that thinks nothorses are extremely tasty.
The small numbers of nothorses that make it across the bridge do not survive long enough to establish a stable population. It gets worse for nothorses when their nemesis makes the jump in the other direction, but at least they have a sizeable population already present so they can maintain their numbers more easily while they adapt (or don't, of course).
For a real-world example, you can look at the restrictions to the range of platypodes in Australia. Their range is curtailed to the West of the continent by the larger presence of crocodiles in the East.
Option 3: Time
There are two main ways land-bridges are commonly formed. The first is a collision of two landmasses due to continental drift. This tends to be relatively permanent on a biological timescale. The second is land beneath the waves that is exposed by falling sea levels, which tends to be more transitory.
Perhaps your land bridge is of the latter type, and has only recently become traversible (say, in the past couple of thousand years). It takes time for population pressures to develop and push an animal to expand their current range.
Nothumans, like their human counterparts, are curious. They seem to like exploring. It's likely that they will make the journey across to find new, untapped resources.
Nothorses, however, are not particularly adventurous. If they're anything like actual horses, 'not particularly adventurous' is a sizeable understatement.
There isn't actually anything at all preventing nothorses from moving across the gap. They just haven't yet.