How far can a 3 year old go?

I think it all depends on the 3-yr old. I'd avoid steep hills, unless there are rocks to climb on, but little ones should be fun. I'd go with a time vs a distance. Two hours should be doable. Be prepared for it to be slow going, because they'll want to stop and see and touch everything. Just have fun with it.

Yeah, it's VERY variable. A rule of thumb is a mile per year of age, but I think at 3 that's optimistic. I like Foxy's answer--plan to go out for a couple of hours, and don't have any expectations about how far you go. You might find an irresistible pile of rocks 200 yards from the car and get no farther--and that's fine. When Second Son was just past 3, we did our first "backpack" when the boys did all their own walking. It was 2 miles and 1000' up from the car, and took 4 hours. Yup, you read that correctly. Lots and lots of time poking things and throwing rocks in the stream. A lunch stop. More snacks than you can imagine.

Worse car scenario is you end up giving him a piggyback ride back. Three year olds aren't that heavy.

In my experience, the distance a three year old can walk varies quite a bit, not only from one child to another, but with the same child from one day to the next. Three year old boys can be quite volatile (at least our boy certainly was), and things can go south at the drop of a hat. We never took our son out at that age without a child carrier, and he was rarely able to hike more than a mile or so, not so much because of physical ability, but whineyness and boredom. Be thinking of motivations that tend to work for him. Our son loves waterfalls, streams to splash in, and dogs to pet, so we look for hikes where any or all of these things might be a possibility. I doubt that sore legs are going to be an issue, he will likely have a complete meltdown long before this happens.

With our son at age three, he had the capacity to hike a small peak, a round-trip of 3½ miles with an elevation gain of 1,587'. There were a few sections on ascent where he preferred the child carrier. On the descent about a half-mile out from the TH he went back in the child carrier. We did this hike several times and he was solo at age 4. The standard time for this hike is 3-4 hours. For us more like 6 hours. He also needed time to rest as well a let loose at a few spots like stream bead or aspen grove to play around. Word of caution on child carriers. They have a tendency to rub on the calves of the youngster as you hike along, especially if the child falls asleep. Recommend long pants and make at home-made fabric wrap with Velcro to cover the outside diameter of exposed aluminum components of the child carrier. Using the hood feature is important also as hats fall off.

We would take our twin girls out in carry packs when they were younger. We would use hiking poles and had them wear their bike helmets in case one of us fell. Were we being overprotective or do others do this too?

Now at five they walk for the most part. Some days they are full of energy and go and go, others they want to go home pretty quickly.

In NY here kids have to wear helmets for riding in the bike trailer so they had the helmets and were very used to them.

We figured that heaven forbid we had a fall with them in the packs they could be brought down hard on a rock or tree trunk.