Chainsaw is a good idea. So is an axe, shovel,and some 4x4 chunks of wood.
Bolt cutter are considered "criminal tools" in some areas. As said above, fence cutting is emergency only.
A Leatherman will cut right through all wire types of fence and barbed wire. Just clamp the wire in the round circle part of the pliers and gently spin the wire, you'll have to bend it to get some leverage. Great for making a pot holder out of coat hangers for your Pepsi can stove.
I use a G31 size optima battery for my aux buss in my truck. Optimas can't explode. An Optima and some good jumper cables, with thier jaws cut to fit the round bar of the lock, will melt right through the lock silently. The key is to make sure your cables and jaws will flow more current than the lock, otherwise your cables will melt instead. Use battery clamps on one end, and make custom spring loaded jaws for the other. Use at least 2G cable. Beside real hefty, custom homemade cables are a ton better for jumpstarting folks anyways. (Note: Science is fun, but this idea is stupid, don't try this)
Your axe will wack a lock off in short order as well.
Gates that aren't chained together can be disassembled with a 13mm wrench. Gates with the fork that get pad locked in place can be bent open. Just bend the fork. Electric gates can be activated by "fishing" your shovel under the other side to activate the other sides metal sensor.
Try to repair the fence, gate, whatever after you pass through. Nooone will notice that you did anything that way, and you'll stay out of trouble.
If you find a fence that's been blown down in a storm, and you clean it up. If it had razor wire or barbed wire leave it there. DO NOT THROW IT IN YOUR TRUCK SO YOU CAN DISPOSE OF IT LATER. Enviro Nazi's have been stringing up razor wire to hurt 4 wheelers and dirtbike riders. Oddly enough they set those traps on legal trails, not the illegal trails dummer riders use/make in parks. If a bunch of riders catch you with razor wire, you best run. Run fast. 800 feet per second fast.