Where are you, Missinsi?
Field hedges (at least in the UK) are generally made largely of tree species, kept small by regular trimming. I don't think poisoning odd plants is going to do much good, as there will always be more trees waiting to grow.
The best thing to do is trim the hedge properly every year or so -- either in the modern conventional manner with a tractor flail, or in the traditional manner by laying it.
Trimming with a flail is best done to an "A" section, wider at the base and narrow at the top. This prevents the hedge becoming leggy at the bottom and congested at the top.
Laying can be done every four or five years, with flailing or other trimming in between. To lay, you let the hedge grow up for a couple of years, then thin heavily, taking out the thickest and most twisted stems completely. The straight stems you lay, weaving between wooden stakes made from the discarded stems and hammered into the hedge. Each of the retained stems is cut nearly through at the base with an angled billhook or axe cut, then hinged down away from the cut. It will grow in this position, making a thick solid hedge.
Field hedges should really only be cut in the autumn and winter.
Cont....