They are all different! It depends largely on whether it is a full loan or a part loan arrangement. Usually full loan means you take on the full financial obligation although many owners will continue with their own insurance as otherwise it can get messy.
Full financial obligation would mean you pay the cost of livery, farriery, feed, hay, straw etc. The owner would usually supply tack, as they obviously retain ownership, although many loaners buy their own bits and pieces (which remain their property after the loan has ended).
Part loan - well, how long is a piece of string! Some owners charge a set amount per week or month and the part-loan has set days when they have sole charge of the horse, and would undertake all stable duties on those days and obviously ride.
I have a pony on part-loan but it is incredibly flexible and casual. The loaner lets me know what days she is free in any given week. I don't take a financial contribution off her (although she has offered) and will muck out/poo pick for me on "her days". This is because he is a young and rather challenging pony and I am just so grateful that someone confident and competent is getting him out and about for me!
Before agreeing to any loan, you need to be crystal clear with the owner what the expectations are and what obligations they expect from you. Some owners, frankly, take the p*ss. If you do agree to the loan arrangement, you would be very wise to have a written loan agreement and don't sign it unless you are happy with it.
In my experience there are far more ponies/horses looking for loaners and sharers than there are loaners and shares so you are in a strong position - albeit your daughter is young and inexperienced. Still - there are ponies out there that have been outgrown and need a jockey but the owners don't want to sell.
As it's a riding school I strongly suspect that any "loan arrangement" will still mean the pony will be used in the school. Take care that you don't end up paying rather a lot for very little exclusive time with the pony.