For the best flat and soft movement, keep her barefoot if you can. Only shoe if you MUST to keep her comfortable and safe… you may be forced to shoe her if she has poor quality feet, or if conditions force you to shoe.
The weight of the steel shoe does classically make for higher action, that’s why racehorses are shod with aluminum (and hunters). However, aluminum does not have the metallic memory of steel, and will spread under pressure- not keep their shape well. Aluminum horseshoes also wear out quickly in abrasive footing- requiring reshoeing often, sometimes before there is enough growth on the hoof for a farrier to work with adequately- thus the classic “bad feet” on TB racehorses- they are often reshod every 4 weeks. The steel shoes spring back into shape better than aluminum ones do, and thus absorb some concussion better. But you get the higher action due to the weight.
If you can stay barefoot, and the horse is happy with that, you avoid all this crap. You avoid losing shoes, having them torn off by over reaching, or ??? You avoid injuries that may occur from brushing/interference, or stepping on the opposite foot (or on your foot). And you avoid a $200 farrier bill every six weeks. If you can avoid shoeing the horse, “bonus” for you and the horse.
If your horse has good feet, and is performing well barefoot, and your workload does not include a lot of work on rocky ground, or slippery mud, at speed, or demands that she work hard for many hours per day and can not take a day off (cowboy on the range working cows or as a pack horse), you may be able to keep her barefoot indefinately. Hoof quality is dependent on lifestyle, quality of farrier work, diet, genetics, and environment. Dry environment and low humidity, and lots of movement helps- not a lot of time spent in stalls.
And yes, mine are barefoot, and compete barefoot, hunters and jumpers. No problems, and nice flat movement, plenty of traction in sand or those fancy engineered footing rings.