You have a nice ligature there and it's a great start. With just a bit of refining I think you'd be there. These comments will reference the first option you posted. I like the gray, just think it needs to be 10-20% darker. It goes well with the blue. I also like the outline, though it could be slightly thinner. Not sure about the little swooshy thing/extra shape on the bottom rule. I think you could have it be a clean rule, and maybe go across the entire portion like the top. You'll have to experiment with it, adding spaces, etc where it would cross other letters. It might just need to stop short similar to how you have it now.
I would also experiment with 2-3 more typefaces for the "quarter horses" text. Needs to be about 40-60 % smaller size in my opinion. Definitey all caps, and maybe spaced out a bit. Try something in Garamond maybe, perhaps a nice clean, light-ish san serif like avenir or helvetica neue or the like. Not opposed to a treatment like Designali posted, though the font is way off there. Needs to be more clean.
Again, great start! these comments are subtle, you are close.