Ivy and horsetail are tough plants to eradicate, as I imagine you already know.
There is some useful information on the web about ivy, including these tips from the Washington Native Plant Society's Ivy OUT and King County Noxious Weed Control. Local garden writer Ann Lovejoy said in the Seattle Post-Intelligencer:
"To safely and steadily get rid of ivy, begin by cutting all vines... If you miss a few stubborn scraps here and there, don't worry about it. Just be sure that none of the vines remain uncut or are left dangling. Now remove all ivy at ground level by pulling strands and prying roots with a small hand-mattock or hori-hori (Japanese farmers' knife). Even if you miss a few roots (as you will), they won't all sprout back. Finally, mulch with a combination of woodchips and compost if you plan to replant soon. If you just want to keep the ground clear for a while, use coarse wood chips for mulch. To keep the mulched area clear, check it two or three times a year. You can quickly remove any new shoots that appear, along with as much root as possible."
The same basic techniques will work for horsetail. The Garden Answers Knowledgebase at millerlibrary.org has the following suggestions:
Here is an article from Oregon State University Extension Service
Here is what Ciscoe Morris said about this plant in the Seattle P-I (April 29, 2006):
"Hands down, horsetail (Equisetum arvense) is the worst weed you can get in your garden. If you've got it, just be glad you weren't gardening in prehistoric times. Back then, horsetail grew to 90 feet tall and you were in danger of being stepped on by a brontosaurus while weeding.
The worst thing about horsetail is the speed with which it returns to make your life miserable after you weed it. No matter how great a weeding job you do, it will be back, practically to full size, within a week!
Do what we did at Seattle University. Plant a mix of shrubs, ground covers and fast-growing perennials that are thick and tall enough to hide the horsetail. Shrubs that hide horsetail include Cistus (rockrose) Lonicera pileata (privet honeysuckle) Lonicera nitida (Box honeysuckle) and rosemary. My favorite perennial to hide horsetail is the prolific hardy Geranium oxonianum 'Claridge Druce.' It will seed all over your garden, but new seedlings are easy to remove in spring. These drought-tolerant plants look great in their own right and because they are so thick and tall, no one will see the hoards of horsetail growing within."
Washington Toxics Coalition recommends controlling it by persistently hand-pulling or hoeing the above-ground growth as soon as it appears. This will weaken the plant over time. It does die back over winter, when you could cover the affected area with black plastic (for a duration of 2 years), but even this may not be entirely successful.
An article by Irene Mills in the Fall 2008 issue of the Northwest Perennial Alliance's Perennial Post says that pulling, digging, and covering with black plastic are a waste of time. The author recommends keeping an eye out in April for emerging spore-bearing stalks, and cutting these off and disposing of them in the garbage. She suggests improving the soil texture (improve drainage, add organic matter, increase soil fertility, and in some cases increase soil pH). She recommends this guide called "Controlling Horsetail" from Swanson's Nursery, originally published in Gardens West by Carol Hall.
Alternatively or in combination with other methods,you might try sheet mulching. Here is a description of that process, written by one of my colleagues here at the Miller Library:
"The general idea is you spread out a layer of cardboard or newspaper (about 4-6 sheets) and then cover that with a layer of organic mulch (compost, straw, alfalfa hay--available at feed stores, wood chips, coffee grounds, etc.). Then wait 6-8 months. This is not an exact science because there are many variables, such as thickness of newspaper, type of mulch and what type of plant you're trying to kill. Perennial weeds and especially coarse grass will push through the cardboard once it starts to break down so it is critical that if and when this happens you pull the mulch back and put down more newspaper/cardboard, and then replace the mulch."