The readiness of a snake to bite while handled/manipulated really isn't of any value in determining whether or not it can do well in a multispecies enclosure.. I worked an exhibit that initially has beaded lizards, western diamond backs, black tailed rattlesnakes and a coachwhip in it for more than a decade. The diamondbacks wouldn't hesitate to attempt to bite me (or other keepers) when every we had to move them (using hooks) but could be tromped over by the beaded lizards without showing any concern at all.
I would however not suggest attempting to house a predator with it's prey species. If it smells like food to many snakes it is automatically food, there are reports in literature (including newspapers) about odd things snakes have been known to eat because it smells like food. These have ranged from reports of attempts to eat ceramic bowls (Kauffield, The Keeper and the Kept) to other items (like this x-ray that ended up in Ripley's museum Ripley's Believe It Or Not - BOADDICTION). This means the garter snake even if it can't reach the frog may be willing to ingest other materials that get scented with the frog.
The snake may indeed attempt to eat the frog even if the snake is too small.
As a final consideration, if the snake is too small to readily predate on the frog, have you considered that the frog may predate on the snake? Even if it can't swallow the whole snake, it may take the tact of other anuran predators and swallow as much as it can initially and then ingest the rest as it digests.
If you need a snake for the exhibit, you would be better off with a snake from the Storeira genus... there are some other possible snakes as well depending on the species that can be used.
Ed
I would however not suggest attempting to house a predator with it's prey species. If it smells like food to many snakes it is automatically food, there are reports in literature (including newspapers) about odd things snakes have been known to eat because it smells like food. These have ranged from reports of attempts to eat ceramic bowls (Kauffield, The Keeper and the Kept) to other items (like this x-ray that ended up in Ripley's museum Ripley's Believe It Or Not - BOADDICTION). This means the garter snake even if it can't reach the frog may be willing to ingest other materials that get scented with the frog.
The snake may indeed attempt to eat the frog even if the snake is too small.
As a final consideration, if the snake is too small to readily predate on the frog, have you considered that the frog may predate on the snake? Even if it can't swallow the whole snake, it may take the tact of other anuran predators and swallow as much as it can initially and then ingest the rest as it digests.
If you need a snake for the exhibit, you would be better off with a snake from the Storeira genus... there are some other possible snakes as well depending on the species that can be used.
Ed
