No need to uninstall CF10 completely. It seems like, you don't have permissions on the hotfix directory mentioned in your post.
I had a similar problem with a CF11 update. I solved it by rebooting the server. That is an OS reboot not just restarting CF.
(Restarting the service did not do it, btw.) I was able to get update 15 uninstalled, but the service still doesn't work. Strangely, I was able to uninstall 15 only after uninstalling 12 and then reinstalling 15. However now I can't install 12 and get a similar error:
FATAL ERROR - E:\ColdFusion10\cfusion\bin\coldfusion.exe (The process cannot access the file because it is being used by another process)
This seems to be the core issue. However, it is not running and I can add and delete test files in that directory. This makes me wonder if there is some sort of lock file which is not going away and making windows think codfusion.exe is in use...
All I can say, is thank goodness we tried this on dev first!
"(Restarting the service did not do it, btw)"
No it will not - You have to restart the box, a sever reboot.
We did a full reboot as well, no dice. Currently awaiting call back from Adobe to work through it.