You can do if you desperately need to, though it's not ideal obviously. I'd either pull it off and possibly go in the school if you have to, or just wait and get re-shod.
Depends on how 'Loose' they are. If they are just a bit clicking then stick to the school or soft ground, If they are really clanking then remove them, or at least don't ride as very loose shoes can slip easily and twist then your in trubs risking a puntured sole etc.
When the farrier is at the yard - get him to show you how to remove a shoe correctly. Always a useful trick to have in your bag !
I'd wait until the farrier had been and then consider if I should shorten the length of time between farrier appointments to prevent it happening again.
As other posters have said stick to good ground close to home if they are not too bad , turnout should be ok if fields are good . Does the horse run around in the field or just put the head down and eat? I would be slow to remove the shoes , even though I can , unless I thought there was a real chance of the horse pulling it off and standing on a nail .
You will probably need the farrier more often , it might help in the future to keep the feet wet by standing in a stream for a while each day and dressing with Aqueous Cream.
My horse had a similare problem when I got him. I took off the shoes because not good for him... Anyway, It's going to be take off by the ferrier so why don't you do it yourself? (But, like the others, be carful)
Working him or not?!, If you horse always had shoes, he will suffer.
Yes, the sole (or more) is kind of not strong anough to tuch the floor. the horse will suffer and you will see it by the way he 'll walk
If you ride - take it easy, be careful of deep going that could pull off the shoe, bear in mind that if you work with loose shoes the risk of a shoe pulling off is great and with that the risk of th ehorse treading on the nails. You also risk stones getting wedged between the hoof and shoe.
Personally I wouldn't ride with loose shoes.
If you are adept with a hammer You could try folding the clenches over a little more to tighten the shoe.