/var/log is probably a bad idea, but deleting the individual logfiles should be OK.
On my laptop, with a smallish SSD disk, I set up
tmpfs mount points, by adding the following lines to
temp /tmp tmpfs rw,mode=1777 0 0
vartmp /var/tmp tmpfs rw,mode=1777 0 0
varlog /var/log tmpfs rw,mode=1777 0 0
This means that nothing in those directories survives a reboot. As far as I can tell, this setup works just fine. Of course, I lose the ability to look at old logs to diagnose any problems that might occur, but I consider that a fair tradeoff for the reduced disk usage.
The only problem I've had is that some programs (most notably APT) want to write their logs into subdirectories of
/var/log and aren't smart enough to create those directories if they don't exist. Adding the line
mkdir /var/log/apt into
/etc/rc.local fixed that particular problem for me; depending on just what software you have installed, you may need to create some other directories too.
(Another possibility would be to create a simple
tar archive containing just the directories, and to untar it into
/var/log at startup to create all the needed directories and set their permissions all at once.)