So how do I set a non default clock rate for an Antminer U1 with Cgminer? For example overclocking from 0781 to 0A81? in Bfgminer I would use this:
bfgminer -o http://your.stratum.server:port/ -u worker.name -p password -S antminer:all --icarus-options 115200:2:2 --set-device antiminer:clock=x0781 --no-submit-stale

In AntMain's version of Cgminer they use this:
cgminer -o stratum+tcp://your.stratum.server:port/ -u worker.name -p password --bmsc-options 115200:20 --bmsc-freq 0781 --no-submit-stale

How do I set a clock rate with Cgminer 3.12.0?

Not from cgminer itself, no.