Texas Pleistocene Rib Bones

[GPayton]

I was searching the gravel bars in the Brazos River just southeast of Houston almost every day last week before the storm hit this weekend. Now the water's too high to look, but I found a pretty good assortment of fossilized Pleistocene aged bones during my trips. Most of what I've found have been fragments that are totally unidentifiable, but a handful still have some significant features that could lead to an ID.

These two are both rib bones, but that's about all I know. The first one I initially thought was from a modern cow due to how clean it was, but after picking it up it was clear that it's definitely a fossil - it's mineralized all the way through and has a decent weight to it. The only animals of that size that could produce such a large rib that I can think of off the top of my head would be either bison or hoses. 

The second bone also looks like a rib, but a lot smaller than the first. It has two deep grooves on either side that seem to match up with pictures I've seen of the origin point in deer and horse ribs where the bone begins to branch away from the vertebral column. 

As always, any help would be appreciated!