We've had some snow/ice storms lately (just a few inches). This makes it really easy to spot every single blackberry plant since most of them still have leaves, while most other things have lost their leaves. Also their stems tend to be perpendicular to the ground, so they stick up above the snow unless the snow is deep.
For smaller plants I like to use my scythe. For bigger plants, I like hedge clippers (hand or powered).
Also if you are wanting to smash them down (e.g. with a board), it is a lot easier to do that when they are covered with snow or ice (due to the weight), and because they are more brittle now (due to the cold).
Great ideas. I grow the thornless ones on purpose. Talk about a low care nutritious plant! The nutrition doctors I listen to say they are as healthy as blueberries, but easier to grow. I also grow blue berries. They produce heavily, even in shady locations.
JohnS
PDX OR
On my former homestead the only candidates for spray herbicide were poison oak & Himalayan blackberry plants. If it were a relatively large patch of Himalayan’s I’d physically remove the bulk of their canes with hand tools; usually long-handled loppers and a shovel.
When ‘dismantling their network,’ I’d follow lead canes to where they’d rooted to start a new ‘clump.’ In the Fall, the long leading cane tips will send out white roots wherever they touch the ground. So wherever they’d re-rooted, starting a ‘new plant,’ I’d dig out that root ball, around the size of my fist.
As you can rarely ever get it all, shoots will generally emerge from the residual roots. Your choice is to dig, or spray them. If close and convenient, I’d dig; if distant (acres away on a hillside), I’d go on a spay mission.
I had neighbors who’d ‘never spray.’ From the city, Brooklyn, NY, they’d heard that ‘spraying was bad.’ Often, I’d agree; hosing down a quarter acre of 8 foot high Himalayan blackberry cane from a 60 gallon tank on the back of a tractor never impressed me. But directly ‘spot spraying’ the cane & leaves of newly emerging and greatly reduced canes using a backpack hand-pump, or, a quart hand-spray bottle appeared harmless, to me.
As years went by, indigenous plants naturally returned to the forest I tended … while across our imaginary property line, previously logged at the same time as mine, my Never-spray Neighbors land consisted of choked fir trees matted and crushed by snow-loaded Himalayan canes and a repository of poison oak. Mine, with open space for the natural reseeding of indigenous understory plants, became a blended canopy of free growing trees ...never in need of spraying again.
They had several - I’d even milk them! They’d make cheese, all organic.
Another neighbor had staked out a goat to do the same; the goat refused to eat anything but the feed they’d eventually bring it… That neighbor eventually executed the goat.. City folk in the country don’t always mix 
We had Government Goats, too. But even deer prefered about anything else to black berries or poison oak ~
I made two long-handled blackberry cutters to reach into the thicket and cut off the canes. This allows the other shrubs to be undisturbed and help shade the root to prevent regrowth of the blackberry. One tool is made of a hand trowel blade and the other is made of a 5-in-1 paint scraper. Handles are made of straight maple or filbert I harvested in the yard. 
Great topic!
It's good clearing them this time of year also because the ground is soft, so tip-rooted brambles come up with less tugging. Still a hard job.
On my 2 acre property, there must have been 1/10 to 1/4 acre of Himalayan Blackberries. I've been clearing them with pruning shears, heavy clothes, and leather gloves. It's a slow process, but gradually I'm getting rid of them. The cleared area gets spread with grass seed and mowed to keep them from regenerating. After a season of mowing, they stop coming back.
I'm not using herbicides because I don't want to kill trees that intermingle with the brambles, and because I don't want wind-drift onto shrubs and trees. I pile up the cut brambles into large berms that are self-composting and will be spread onto vegetable garden, and I worry about residual affecting my kitchen garden. The brambles will be a good source of compost in a year or two. The vines are soft and break down fairly fast.
John I'm also growing some thornless or almost-thornless blackberries. I have Prime-Ark Freedom, Ebony King, and Columbia Star, if it survives being uprooted by deer. I need to move them to a deer cage because the critters love eating them without the thorns. I got a few the first year on Prime Ark Freedom which are a primo-cane bearing variety, but deer ate most of those too. Huge berries.
Goats are definitely an animal that need to be trained/managed/handled. My children refuse to go work in the yard, even for money. They act as if it's some unspeakable indignity to work in the yard. And yet I do it all the time for fun and to help feed the family.
There is a lady in the Portland metro area who rents out goats for this purpose specifically. Apparently it is not actually good for the goat to give it soft "human" food all the time. They do better on tougher food like vines, twigs and branches. Kind of like us humans eating white flour, salt, fat and sugar instead of fruit, vegetables and berries!
I live in a suburban area, so I don't have to worry about the deer. Coyotes don't eat the berries and fruit, and can't jump the fences apparently.
I always liked to cut the thorny vines down and move them away. Then I could get at the roots more easily, which don't have thorns. Now I just stay on top of them, which is easy, because I don't have acreage.
I actually have used some of my excess dead canes as an experiment for growing mushrooms. We'll see how it grows....:). Dead thornless canes, pasteurized, then put in buckets with white elm oyster mushrooms.
John S
PDX OR
John, That is an amazing idea! I hope it works.
My neighbors gave me unsolicited advice and recommended goats. I actually think it's good for me, mind body and soul, to be out in nature doing thst job. Makes me feel one with nature. There are Douglas Hawthorns mixed in with the brambles, mostly fallen over. Those get cut for firewood. I planted some trees in the cleared area, and the next part will be kitchen garden. More reasons not to use herbicides although goats might fertilize the area if we used them.
I should be done with my kitchen project next week. Weather permitting, that means get back to cutting blackberries.
John - I was thinking about your problem. How to get kids to do yard work. Here are some ideas.
1. Tell them you hid a new cell phone in the leaves, and they will have to rake them up to find it. Or in the blackberries. Or buried in the vegetable garden.
2. Contact Nintendo and ask them to create a "Pokemon Yard App" in which they find Pokemon characters by digging or raking.
3. Have their internet and cell phone signals blocked. Tell them the device that releases the signal is in the yard under those leaves or buried.
I grew up in a Midwest farm family. Our idea of fun was working through corn rows with a hoe to pull out weed grasses that were missed by the tractor. Looking down the clean row was its own reward. That was before Roundup and Roundup Ready. Being around me is like being around your grandpa who reminds you he had to walk 2 miles in the snow to school wearing shoes with holes in them, uphill both ways. 
I like the ideas Daniel. Some people have told me that over time, they tend to pick up on the habits that you did that actually worked for you and will work for them as they see it. Makes sense to me.
I grew up in an urban, intellectual family here in Portland. I rebelled by enjoying nature, outdoor sports, gardening, and active outside work. I'm like the same grandpa you are.
On your Douglas hawthorns, I dare you to chop them to about one foot and then graft or bud pears onto them the next season. Works for me. Or graft better tasting, larger hawthorns like the Carriere hawthorn.
JohN S
PDX OR
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