Is the Horse resource inside your culutral boundaries?
If it is not, you will need to convert a worker into a colony. A colony will make that tile 'yours' for a while. Colonies can be asborbed by any culture (even yours), so they are not a good long term solution. Plus, if an enemy AI ends its turn on the road that connects you to that colony, the supply line is broken. In the case of a strategic resource (like Horses) that means you cannot start any new Horse units until the supply line is clear again, though this does not affect any units currently in production; they will continue to be built. If the resources is a luxury (Wines, Spices, etc) then you could lose the happiness benefit of those luxuries.
Trading Reputation
One thing that can be hard to grasp is 'Trading Reputation'. If it is good, other AIs will be willing to make trades with that involve you sending them Good Per Turn. The goods could be a luxry, a strategic resource, or gold. If your trading rep is bad or broken, then your trade options are limited to cash and techs on hand at the time of the trade.
At the start of the game, your trading rep is good; or at least not bad. If you make a trade deal of any sort and keep your end of the bargain for those 20 turns, your trade rep stays good. If you break it, then your trading rep is busted.
That makes sense.
However, what others have found out is that you can be held at fault for breaking a trade deal even if you did not cause the trade deal to be broken. For instance, you have a trade deal with Rome, Spices for 2 gold per turn. You are providing the Spices. You have only one road that connects you to Rome and it goes through neutral ground. Rome is at war with India and you are not. If an Indian unit ends its turn anywhere on that road, it will break the connection between you and Rome. And your trade rep takes the hit. It is not your fault, but you get blamed for it.
If all your trades are one time affairs (100 gold for Bronze Working or just trading techs) you don't have to worry about your trading reputation. All other deals, the ones extend over multiple turns, do affect your trading rep. Not just you sending gold per turn to a civ, or luxuries or resources. Rights of Passage, Military Alliances and Peace Treaties are also used to measure your trading rep.
Don't even consider signing a Mutual Protection Pact, at least not for a while. Those things are a great way to get involved in wars you do not want nor need.