Looks like a good start. I'd say play the deck a few times and make a note of what works for you and what doesn't. Having been playing around with something similar recently, here are a few of my thoughts:
You might find that opportunities to play Ridden Down don't come up that often, in which case trading one or two for This'll Hurt in the Mornin' might be useful to get more Cheatin' Resolutions, or possibly Rumors to make it harder for your opponent to deny your income and defend their deeds. If you find yourself playing against a lot of Desolation Row decks then Bounty Hunter might be useful, but unless you've got reliable ways of placing bounties on people I'd avoid it.
You might find that for the first couple of turns you don't have the ghost rock to spare for the horses. The Morgan home ability gets around that with its discount on deeds, and the above mentioned William Specks would also be handy for kickstarting your economy while allowing your dudes to saddle up early on. I like adding in a Roan for a cheap option to enable Lane and Jarrett to do their thing, and they can trade for a better horse later on.
If you're looking to pick off specific targets, Pinned Down would be useful to complement your Kidnappin and Run 'em Down attacks. However, it does have the problem of sharing the same value as those two actions. Using Run 'em Down when you've got Rope & Ride in your hand should be a good enough way to achieve the same outcome.
As long as you pick your fights carefully, the looser draw structure shouldn't be an issue.