I wouldn’t do anything crazy, but as long as the horse has good feet and isn’t lame/stepping off it shouldn’t be a big deal. Especially if the footing is soft— I definitely wouldn’t suggest going hacking/riding in an arena with rocky footing or anything like that. It’s always best to check with a trainer/vet/farrier before doing so though, as you don’t want to cause any more damage :) just make sure to get the shoe back on as soon as possible!
My pony lost her front left shoe and I continued to ride her after lunging her and see if she was okay on it and she was perfect when I was riding her. So depending on your horse and area I think it would be okay for a while :)
Really depends, generally if a horse has thrown a front shoe i will try not to but unless the foot is damaged if a horse has thrown a back shoe i would still be pretty happy to give it a horse a light ride on a soft surface like a sand arena.
I wouldn’t as my horses’ breed is known for shocking feet - even though there’s is fine I put it down to good, consistent farrier attention.
It’s up to the horse really, if you ride on a surface it shouldn’t be too bad however I would avoid roads and Riding on hard ground. But the chance of injury increases when you ride with a shoe off due to reduced ballence and support on the hoof