We have this all over our lawn and garden. I've dug out the lawn as it was full of moss and horsetails. I guess this indicates how poor the soil is. The roots go far deeper than any herbicide will be able to reach. Glyphosate won't work. There are other threads on here where people have said they have used it to no avail. Glyphosate actually encourages field horsetail by eliminating competing plants. Horsetails (and they are called horsetails, not marestails...which are a different plant that grows in water) love poor drainage, low oxygen, and acidic soil.
You need to improve your soil by applying lime. After AT LEAST two weeks, apply horse manure. Then some nice compost. I've tried killing them with industrial grade vinegar (20%) but, like anything applied to them, it will only kill the tops and do nothing for the roots (which can go as far down as 7 meters...or over to Japan). Also, it acidifies the soil.
Covering any parts of your garden with membrane or plastic will just make the roots really happy without the oxygen and horsetails will pop out everywhere along the sides. Don't do it. That's what the previous owner did here. You lift up the sheet of plastic and it is nothing but horsetail roots under there. They don't like shade so you can crowd some of them out with taller plants.
From March to May you must be very vigilant and pull out any female (the one in the photo is a female) horsetails as soon as possible as they spread thousands of spores everywhere. If you can, pick them up in a plastic baggie to contain the spores and landfill those suckers. Do not till as it will make things worse. Every bit of root will regenerate into a new plant.
We need to realise that they may never, ever fully go away. They take a lot of silicone from your soil so you can compost them after drying them out in order the replace the silicone. Try to improve your drainage by sloping the land away from your property and adding some ditches for the water to flow down. Some simply say it is best to pull out what you can and then just deal with them.
The roots go so far down that they don't compete too much with plants for nutrients (allegedly) and the best thing to do is encourage them to move along by improving the soil. Very hard to do if your neighbour has them.