Your horse could certaily go barefoot. I would wait until the main riding season is over before pulling shoes, though. She might be tender at first and you don't want to miss any rides by changing in the middle of the season, also, newly bare feet need time to adjust to just carrying the horse, the transition will go faster if you don't ride her right away without some sort of protection, like boots.
What I see, (first, I pick at the hinds) is the toe needs to be beveled a tad more in the hinds, you can see the wall has a bit of separation in the sole view, it's trying to chip itself off where the bevel should be done. Hooves are wonderful about telling you what they need! But they look good other than that, and that separation I speak of, would be an ugly chip, but superficial that wouldn't cause lameness, but it's not something you want to let happen, when it's so easy to prevent.
The fronts...again, I pick! The Left Front, while it at least doesn't have the degree of flaring as the right, it is still there, and you can see how the farrier has rasped off the toe trying to fix it or make it look less obvious, or even trying to make it fit the shoe, but I'm going to give him/her benefit of the doubt and say they are attempting to remove the flare before it gets worse. Her heels are lower on that foot, she will probably always have lower heels on that foot compared to the other front. Not a big deal, as most horses are NOT perfectly symetrical, and sometimes it's a conformational reason up higher in the leg, like her other leg could actually be shorter, so the hooves grow at slightly different heights/ angles to compensate, and it doesn't cause any problems, but forcing the hooves to match would. Or in her case, she may just need the other foot trimmed a little different and they will even out themselves.
The right front, has a signifigant flare at the toe, causing the heels to squeeze together and be higher than they should be for that hoof. Initially, a really steep bevel at the toe when the shoe comes off will help stop that flare, and by the next trim, it should be growing out. Initially, leave the heels alone, and focus on the toe, or your horse will be very tender. Too many changes at once can cause more set backs than necessary. So correct the toe/flare first, and the heels will start to show when they are ready to come down. She will be more tender on this foot than the other, as the flare pulling the foot forward has distorted the sole a little, making it a tad flatter than normal, but in a few trims, if done right, that will go away.
I'd suggest getting a barefoot trimmer to to pull the shoes this winter and set you up in some boots, so you won't have to miss any rides. The more you exercise her, the better her feet will get, with proper trims. By next spring she could be going quite well barefoot, and you will find you use the boots less and less.
And for jumping, I think someone mentioned it? YES you CAN jump barefoot. The hooves will have to kept on a good maitenance schedule to prevent chipping, the slighest bit of extra hoof is more prone to breakage with that sort of stress, but keeping the growth in check is the key.