Could it be that those "few hours walk in the woods" exceeded her range (both in physical endurance and attention span) pretty much from the get-go, so you ended up always carrying her towards the end of the hike?
(I got kids age 12 and 8 who get bored of a "hike" in much less than "a few hours". They can run around the playground, and do visits to the museum or the zoo for almost a whole day, but a "plain" hike would bore them witless.)
If your kid never experienced "making it through" a hike, thus making the hike itself something to take satisfaction in, she won't be eager to put significant energy into it, and will ask to be carried as soon as she feels like she's exerting herself -- because, what is the point in walking longer if, in the end, you'll carry her anyway, and she'll still get to look for fairies or explore the playground?
I think the trick here is to start small, let her achieve "completion" on a regular basis, and then extend things as her endurance, attention span, and willingness to exercise herself increases as she grows up.
One thing more, I don't think the average three-year-old needs artificial "workout" or "exercise". Usually their play instinct has them moving around pretty much non-stop anyway, inside or outside the house, and they have a rather fine-tuned feel for when they want to move, and when they want to rest. IMHO, it's better not to tamper with that too early in their life, but instead heighten their awareness for what their body tells them.
Plus, physical strain (which we grown-ups would label "exercise", "training", or "workout") can easily be actively harmful to young kids. Their bodies are already developing rapidly towards greater strength and endurance, at huge stress to their system, without any additional "load" from us adults.