Translation:I stop the traffic because there is a horse on the road.
"I stop traffic" and "I stop the traffic" mean two subtly different things. "The traffic" refers to the traffic at a specific place/area or time. "Traffic" alone is more general. It's hard to know exactly how to translate from Dutch to English in this case without context.
As a Canadian, I find "in the road" and "on the road" interchangeable in contexts such as the above.
Though I might be more likely to say "They parked the car in the road" (as opposed to in a parking lot or perhaps leaving the car in a ditch).
In contrast to something like "get off the road", "the kids were playing on the road" would make sense. However, note that "the kids were playing in the street".
Additionally, "they left the car on the side of the road" not "in the side of the road" and "I am standing in the middle of the road/street" not "on the middle of the road/street".
Fundamentally, I think whether it's "on the road" or "in the road" is simply based on regional dialect as well as how the person is visualizing what they are describing.
As you can see from the comments above, not everyone agrees on the translations for "on the road, in the way, in the street" etc. "Op de weg" translates to "on the road", and "in de weg" translates to "in the way". Anything that is an obstruction is "in the way", or "in de weg", both in Dutch and English. A horse can be "on the road" without being "in the way". Hmmm. It's tricky to explain. Not sure if this helps you.
I would translate your sentence as "I stop the traffic because a horse is sitting on the road". I would have used the present continuous in your original translation as well - i.e. a horse is standing on the road - but only because it sounds more natural, not because there's anything wrong with your sentence.