LHP is right. Wire panels that have been welded at the joints like that (and like hog panels and bull panels too) are not safe to use in a roundpen where you will be working horses. It's not just because they are not sturdy enough either.
I can tell you from personal experience that if a horse happens to crash into one of those panels, the welds will pop and then you'll have nothing more than a mess of thick wires pointing out in every direction just waiting to hook onto tack, skin, and/or impale a horse. My Dobe has a very large scar on his belly from where he got impaled after trying to jump through and crashing down on the top of a fence made of panels just like that.
As for the t-posts and a horse getting impaled on them, yep, it can happen. If a horse tries to jump out, that wire isn't strong enough to not bend...and it will bend down over the top of the t-post, or it will come apart at the welds. Either way, exposing the top of the t-posts.
A pen like that would work fine for housing a calm/gentle horse, but I wouldn't work a young horse in there.