Using slapt-get I've done it gradually, just in case. So I've done 12.0 -> 12.1, 12.1 -> 12.2.
slapt-get is not officially supported, it is a third party tool. If you use it, complain to its developers. Canonical Slackware users do not use third-party tools for upgrading. They use their brain. When a new Slackware version is released, it contains an UPGRADE.TXT file. Those are high-quality instructions for manual upgrade. Follow them and do the upgrade by hand, do not let a third party tool screw up your system.
After Googling for the subject I've stumbled upon someone that did a kernel upgrade from 12.1 to 13.0 and he's complaining about /dev/hda being switched to /dev/sda.
linuxquestions.org is a place for newbies. Do not blindly take their word for everything. Read the official Slackware docs. A Slackware 13.0 default kernel works fine with /dev/hda names. I can vouch for that because I'm running Slackware 13.0 on a computer that has an IDE drive. The transition to /dev/sda* is made only in Slackware-current, which is not Slackware 13.0. Relevant quote from the ChangeLog:
Mon Jan 4 21:43:02 UTC 2010
New kernels... and this deserves a mention/warning: the last bits of the
"old" IDE/ATA system have been removed now. Everything should be using
the libata based drivers now, so if you have any drives that are currently
running as /dev/hda, /dev/hdb, etc., when you reboot with these kernels all
drives will be renamed as /dev/sda, /dev/sdb, etc. If you had any /dev/sd*
already, they might get renamed. Adjustments may be required in
/etc/lilo.conf, /etc/fstab, the initrd, and elsewhere. Good luck!
Again, this is not 13.0, this is the bleeding-edge -current, which you wouldn't want to have running on your server anyway. -current is for testing purposes, it's being polished until it becomes stable and usable.