I've had my bike locker handle freeze up many times just like the OP. I always carry a small container of WD40 and a flat head screwdriver in the winter. I can work the screwdriver into the gap between the handle and the rest of the metal around it to wiggle the handle some and squirt the WD40 in there. Between that and kicking the hell out of it with my boot, it has always come free.
I have had a tougher time with frozen u-locks. I've tried the heated key technique and various lubes, but sometimes those locks just freeze solid if there was any moisture in them.