I am not one dislike remote place, country site and simple living and I am not overly fond of metropolitan life. But when I have to spend in some places with fireplace, piles of firewood, some wild natured domestic animals which are potentially unsafe for my wandering, curious, active toddlers, we parents have to watch them at all times. Are we overreacting? Do we let them explore new environment with their own even if there might be small fell-offs, bruises?
As commenters have pointed out, the question leaves room for interpretation. I empathize with the sentiment though, which is why I'll give a shot at answering by way of an analogy.
We have a 2.5-year old daughter. We live in a very urban, vertical city condo that has five floors. For almost a year now, since she was a little over 18 months, she's been able to navigate all the stairs safely to the point where we've not bothered to use the baby gates at since that time. I was ambivalent about even installing them in the first place, but my wife had insisted. In hindsight it made parenting a little easier between 15 and 18 months but wasn't critical. The way we taught her was to let her get up to the stairs time and time again from the time she could crawl and watch her at the edge of the stairs. She was never unsafe on her own, but she needed guidance. We showed her how to turn around and crawl down backwards. It took her a half dozen attempts to feel for the steps with her feet when she couldn't see them. We explained the dangers to her of not using proper technique. At first that was crawling down backwards. Then, when she wanted to walk down, it was always holding onto the wall. She tumbled a few steps once or twice. That's what it took to the road of mastery.
As a toddler she became a far quicker study. So, my answer and advice for your examples would be the following: take them up to the fireplace. Explain how it works and where the dangers are. Let them feel the heat. Ask them to point out to you what parts are dangerous and we they can't do near the fireplace. Trust in their intelligence and desire to learn. Watch them carefully the next few times they approach on their own. Be ready to intervene but let them drive. When you've convinced yourself they'll be safe, relax.
For the piles of firewood I'd stage a demonstration of logs tumbling down when climbed upon.
The same goes for the animals. Show the kids when it's safe and when it's not safe to approach them or how. Perhaps the big ones are always dangerous. Tell them they can't approach without an adult. Tell them the animal is heavy and could hurt them. Show them where to seek safety.
Another example: Our daughter loves dogs at the dog park. We've taught her not all dogs are friendly and she can't just go pet them. Now she approaches carefully with her hands extended so the dog can sniff her. An adult is always near, though.
Hope it's useful. Your instinct to want to protect them is legit. The answer can neither be full freedom nor full prohibition. They're adaptable little creatures and learn fast.