Yes they do!!!!

When I got rid of my boy(Pardo) my sister and I were very particular about who he went to. Many came, and one lot left and we just cried and said "They're not having him!!!!"
One lady came, quite slight(Pardo had an attitude, not mean, just too big for his boots), and I thought"hmmm ok we'll see" She was looking at him as he had been raised the natural horsemanship way. the first thing she said was I prefer to ride my horses in a halter(headstall) wow I thought, so I said thats all we ride him in.
We saddled him up and off she went. It was blowing a gale,and pouring with rain, not the best time to try a new horse. He jigged around for about 5 minutes, then you could almost see him sigh and say "ok she knows what shes doing"
I think my sister and I cried when she left, she was an answer to prayers, kind loving and gentle. We went out and saw the Natural riding school he was going to and wow, what a place, all horses fat, happy and very well behaved, in paddocks full of grass.
We've driven past once and he looked happy.
Sorry to go on, but I still grieve about him, in fact I'm crying now!!!!
So I understand about your saddle and horse trailer. I've got his halter and lead hanging in my lounge room........................couldn't bear to get rid of all of him!!
Kate
ps sorry to hijack the thread!!!!! :-)