Foraging in woods and poisonous plants

False Solomons Seal should be ok. True Solomons Seal is toxic. False Solomon Seal: Pictures, Flowers, Leaves & Identification | Maianthemum racemosum
If it's any comfort, we have true Solomons Seal in our woods, and my goats have most probably grabbed bites of it from time to time. They are all fine.
If you have a high concentration of toxic plants in one area, you may not want to let your goats out there to browse. However, I no longer worry too much about them when there are lots of non toxic foods available. Make sure you give them some hay before you let them out to browse the first few times, so that hunger doesn't push them to eat something they shouldn't. Many toxic plants are not lethal, or even particularly harmful, in small doses. Goats tend to snatches bites here and there, so if they get something mildly toxic, they may not show any ill effects, but it may cause enough of a reaction to make them avoid it in future. It is good to educate yourself on the lethally toxic plants in your area and try to avoid those. For the rest, the goats will have to begin learning what to eat and what not to. They are smart, and they will teach each other and their kids. It is always good to have activated charcoal and milk of magnesia on hand in case you suspect poisoning.
If it's any comfort, I have had my goats foraging around our property for about 4 years now, and never had one seriously sick because of something toxic that they ate.

Great advice from @Cedarwinds Farm ! Agreed about solomon's seal. The false SS is edible; people here drive slowly in the spring and collect it from our ditches. It's pretty good!

That's how I approach it too. Some people (especially with mineral buffet/cafeteria style feeders) put free choice charcoal out too. I don't know that I'd do that ALL the time, but sometimes maybe.

We have a lot of native milkweed in our pastures, supposedly toxic to sheep and goats, and our sheep eat it pretty quickly when going into new pastures. I think they are self-medicating with milkweed; my hunch is it's mildly anti-parasitic. Still, we go in the fall and pluck all the pods off that we can so it doesn't proliferate too much. There's a lot more here than used to be (yay monarchs!).

I remember we live near each other...I'm in Cottage Grove, south east of Madison. Are you a couple of hours north? Our ruminants have nearly cleared out the invasives from our woods! It's pretty exciting! Honeysuckle and poison ivy are dead and gone, garlic mustard limping along.

I have some milkweed growing out in our meadow too. We first noticed it in the back of one of the horse rotation pastures. I fed a few to my goats trying to get them to eat it (after all, they are supposed to clean up the weeds in the pasture, right? 😅)
They took a couple bites and knew it wasn’t good for them. 🤷🏼‍♀️
after I then identified the plant and knew what we had (and that it wasn’t good to have livestock eat it) I just pulled all the plants from the horse pasture, but left a nice stand of it in the corner of the meadow for my honey bees and the monarchs.
It was way too hard to try and dig up the rhizomes! I just snapped them off at the base and went back out a few weeks later intending on pulling any that regrew. It didn’t really… so I figure I’ll just keep getting it beginning of season and eventually it’ll stop returning. Just in the horse pasture. Lol

I heard about a FB page, I'm sure there are multiple ones, but the one I joined was Plant Identification - post a picture and your location and the experts (like here!) will weigh in on what it is. I've used it before, they are very helpful - sometimes they argue over whether a tree is a plant, but I just sit back and enjoy!

I used to worry a lot when I started walking the girls deeper in the woods, but as other said, they are pretty smart. I've learned the types of leaves they love and they have no issues with. And I've learned what poison oak looks like and that while they love it, I am highly allergic to it! And if they do eat something I think might be fishy, I do make sure I give them fresh hay to try to negate any negative side effects.

And then there's the neighbor that chopped down their cherry tree and the girls had nibbled on it, I thought I'd be a good neighbor and make sure they were good with them eating it and then she said, they can't eat that - after about 3 days of them taking a couple bites! They didn't eat that much and they had survived the first couple days of my ignorance, so all good!

Enjoy your walks!