THANK YOU! You give me hope that there are still horse owners out there who care about their land. (Conservationists have a notoriously hard time getting through to horse owners, as a general rule, since they are so steadfast in many of their ways.)
I have never been to the Eastern side of the country, so there are some differences and issues that I have no clue about, but as for what I can help with:
1. land bordering conservation land will vary based on the easment situation. As a general rule, wetlands and riparian areas should be protected, even if they are not in a formal conservation easment. Planting dense stands of grasses and shrubs and fencing it off from grazing can work well in these cases (50 to 100 feet, ideally). Spot spraying in there with a wetland-safe herbicide on occasion can help keep weeds from establishing. If you need to let the animals get to a stream to water if there are no off stream watering facilities, a water crossing should be constructed so they will not stir up the stream bottom or erode the banks too badly.
2. oh boy, mud management. I don't have a real good answer and have been trying to research this myself. I know installing french drains can help, but they are tricky to get just right and require maintenance. Sometimes the best answer is to pick a safe sacrifice pasture and let them tear it up while protecting the rest.
3. It really depends on what product(s) was used. some are very narrow spectrum and water soluble, and a season of rain will do away with or neutralize them into their neutral components.
4. Gardeners and viticulturists could use composted manure. The key is thorough and proper composting, which there is TONS of great literature on. Basics include balancing browns (carbon) and greens (nitrogen) and keeping the air and water flowing to get those microbes working. Hint, if it smells bad, something is wrong. AND if you are in an area with high precipitation, porous soils, or a high or vulnerable water table, please store and compost manure over cement and covered
5. Integrated Pest Management (IPM) is the use of combined efforts to control pest species (animal or plant). These vary for the situation and target species, but generally include scouting, spot spraying with selected products (usually narrow spectrum, low risk pesticides, some organic approved, such as sulfur powder) and introducing natural predators (with caution). I can't comment on Japanese Knotweed, but i know it's a bad one and very hard to erradicate. On a side note (I just had this convo with a transitioning organic farmer today), sometimes a land is so over run with introduced species and invasives that there is little you can do without chemical intervention. In this case it was an annual invasive grass which comes back with a vengence when burnt and out competes the natives here. We decided that it was best to carefully apply pesticides for a year, then transition to organic IPM measures. Nothing will be harvested, but the hay will be mulched into the soil to increase biotic activity to breakdown any residues and get them on the road to organic certification.
6. Topo maps! They will give you more info than you know what to do with. By studying them you can understand where you sit within a water basin and will understand where water flows off of your property, too.
7. Well, i spend hours per day calculating this with a program called RUSLE2, but it is trickier on pasture land than on crop land. I would focus on keeping your soil covered. Soil erodes by water or by wind. Water is broken down into sheet, rill and gully erosion. In sheet erosion, which causes the most loss, surprisingly, the soil is detatched and carried away by individual rain drops. To prevent this, the soil needs a cover (grass, mulch) rill and gully erosion are from concentrated flow of water and are hard to prevent. Good drainage will help though. Wind erosion can be prevented by, again, keeping the soil covered with grass or mulch and adding wind rows to break up the wind.
If you are interested in your soil, check out Web Soil Survey - Home
you can pull up an area, see the soils, and look at soil reports to learn more about it.
Good luck on the land search! I'm currently looking for property as well to keep my horses and a herd of meat goats and meat rabbits as well as a subsistence garden.