My parents both love the outdoors, and we went camping and hiking a lot when I was a kid. My parents divorced, and my dad later remarried. My step-mother didn't like to camp, but we still went hiking a lot. My step-sister (7 years younger than me, from here on my "sister") HATED hiking. She was always way in the back saying, "Can we go home yet?" She was miserable, we were miserable, and she was so SLOW.
Then one year when my sister was in high school she and I were brainstorming about what to get my dad for father's day, and we decided upon a family hike up a mountain with the added bonus that my sister would not compalin even once. My dad was incredulous; he did not think she could do it. So we set off on this Father's Day hike, and my sister was up in front with me. I think her attitude was, "let's be fast and just get this thing over with if I'm not evey allowed to complain." We were booking it up the mountain, talking the whole time, and about halfway up my sister said, "You know what? It's a lot more fun when I'm not complaining the whole time." Now my sister loves to hike, and she has voluntarily gone hiking with me on several occasions!
My 4-year-old son also has a bad habit of complaining about things. He will decide he's not going to have fun somewhere and then proceed to make himself and everyone else miserable. We're talking a lot these days about how you can decide to have fun or not to have fun, and it will come true. So much of life is about your attitude. I'm not sure yet whether this is something you can teach someone or whether you really have to learn it on your own, as my sister did. And I'm sure that my sister's miraculous about-face with regard to hiking would not have happened for everyone. Maybe you can't get your daughter to really love being outside, but if she has to be out there with the rest of the family, then surely there are ways to make it bearable for her. But it has to start with her desire to have fun.
Maybe you can work out a deal where she gives you a certain amount of outside time where she pretends to have fun in exchange for your letting her stay inside for a certain period of time. Maybe you even stay inside with her and pretend to have fun in exchange. Perhaps everyone will start really having fun while they're pretending!