So, what confuses me here is that the wizard is capable of creating an ice bridge (with ice magic) and then melting it (with fire magic). Can't he just freeze/burn the bear? Does he feel like killing a bear is morally dubious?
Anyway, doing puzzles that are solved with fire & ice can be a fun gimmick.
To avoid rambling, I'd say think about:
- The Wizard's Motivation.
Why is he traveling the world? Is there a destination? How you answer this can give you some idea of where to put puzzles (and maybe what kind, too). - Types of Puzzles.
Your example makes it seem like the puzzles will be trying to solve conflicts with logic (using the magic). If that's right, just think of more conflicts based on where the wizard is going, and see what solutions you can come up with. - Magic System.
There are lots of ways to handle magic, but generally consider if there are limitations and what they might be. Having the reader know what the limitations are can help inform their choices when trying to solve puzzles, but you knowing the limitations can also help you come up with the puzzles.
Regarding examples, I'll leave it up to more creative folk. Mizal's idea is certainly not an obvious one, aha.