BSDfan666's recommendation of a USB device is an excellent one; the entire OS will fit nicely on a 512MB stick, though a more modern stick (with more storage) would be recommended, to eliminate the write-lifespan-limitations of earlier technology, and allow the installation of packages. Or an external USB disk drive could be used. USB storage devices appear as SCSI hard drives to the OS (sd0, sd1, ...), and if your BIOS allows, could be bootable. If not, you could still boot from floppy or CD, yet have your root and other partitions remain on USB.
Another option is a LiveCD. I offer six different ISOs for different purposes, one of which might meet your needs. (The 4.5-release versions are in beta test and available, if interested.)
There were a lot of LiveCD versions of OpenBSD over the years, as far as I know, mine and Stephan Rickauer's (
bsdanywhere.org) are the only general purpose ones that are maintained. Stephan has a much cooler website than I do ... his is very pretty, mine is just some static pages written with OpenOffice. We've traded technical information; much that we do under the covers is similar, though we have different goals in mind.
(There is one special purpose LiveCD that is also maintained and supported. It's called LOCKSS, and is used in library preservation. See www.lockss.org for info.)