Hi Deanne,
Welcome to the forums.
I like your 2nd photo. I would have cropped it a bit tighter (at least to get rid of the piece of tree trunk on the left) and maybe edited out the fence in the background. I think I'd add a tad bit more contrast too. But overall I like it. It tells a story. For me, it looks like a pony coming home for dinner after enjoying some playtime.
I don't care for the first photo. The back ground is distracting and it looks like a simple candid shot.
The third image is nice but you should be mindful of the fence line in the background. You'll want to try to keep it as level as possible.
The 4th is a nice photo too. Looks like you've captured playtime.
You mentioned that you are new to photography. In that case, I would say you are off to an excellent start. Looks like you have an eye for composition. You'll want to read your new cameras manual forward and backward...and then backward and forward to get the best out of it. Good luck! and, again, welcome!