The trailer tie you bought will be just fine. That really all you want so the horse can reach the manger and not completely restrict head movement. If its a straight load it really doesnt matter as long as on the opposite side you have hay or something to help balance the weight..If it is a slant load trailer which ever side is closer it is to you. I couldn't remember what trailer style you had. My bad..haha
I've hauled horses over 1000 miles in one trip.. trust me trailer ties are a must. The one the one that you got will do just fine.
Good luck on your trip