Yes, it is possible to root the SE Xperia X10 mini. I'm not sure if I have successfully rooted my device or not, but I have installed SuperUser. Considering you can install SU on rooted devices only (I think), it should be rooted.
Anyway, I found this script for rooting Xperia X10 Mini Pro on xda-developers, but it worked for me too. Unfortunately, I cannot yet post links here, or I would've given you the link to the script.
Search for "[ROOT] x10 Mini Pro" on xda-developers, and you should be there.