Certainly you can; in fact, if you're not going to use it immediately, doing so is probably a good idea.
Things that would be a bad idea:
- Putting it in a sealed, airtight ice chest.
- Keeping it in an unsealed, non-airtight ice chest with you (or anyone else) in a sealed, reasonably airtight enclosure, or even an open one if the openings to the outside air are above head height.
- Mixing it up with your regular ice chest and putting chunks of dry ice in your soft drinks. (Actually, this could be a great idea, but you want to be sure you don't tilt the glass so far the dry ice touches your lips.)
- Messing around with dry ice in general without insulated gloves ... due to the Leidenfrost effect you may be able to get away with this if you're careful, but use the gloves anyway.
