Of course you can do that with mice if not too many, say to give one adult mouse to full grown frog , no problems here, worms no problems either, they are easily digested. Im talking about healthy frogs that would take it on their own.
Babies are different story here.
Common sense is needed and if for experienced keeper it is ok to bend rules, for not-so-much experienced keeper it is better to follow them and that is why i always advise that is better to be safe then sorry.
With a garter snake or any snake for that matter... It is no for many reasons, ethical included. It is very hard to digest prey, long item. Frog cant bite a piece of it when he cant fit anymore but will swallow until is done with very high possibility of having big problems soon after.