This comment from /r/UnresolvedMysteries makes an interesting claim about women hiking during the 1940s, and one woman in particular. The comment says:

Seriously, the thing I'm having the hardest time picturing is a young woman of that era being an avid hiker. I know that sounds sexist, and I'm a woman, but I can't imagine her routinely lacing up her New Balance hikers and going out for a multi-mile hike alone.

While I'll agree that there is a perception that women weren't necessarily active in outdoors life, the reality is quite the opposite. Women have a long and illustrious tradition of being involved in hiking, conservation, exploration, and general outdoors activities. The late 1940s in particular was an era in which women's involvement in sports like rock climbing was exploding as the sports grew in popularity and accessibility.

As far as general outdoorsiness is concerned, there's a long and illustrious history of American women becoming enamoured with the environment around them. This article, for instance, compiles numerous stories of women throughout the 19th and 20th centuries who could be considered to be as much at home in nature as Thoreau, Audubon, or Muir. The activities they participated in, too, are as adventurous, if not moreso, than many men. Georgie Clark White, for instance, became the first person to swim the Colorado River through the Grand Canyon, and 1953 saw the first Western all-women's climb of Gyalgen Peak in Nepal. Even in the early 1940s, surfing was beginning to be a gender-integrated activity, demonstrating the increased accessibility of outdoors activities for women. Before the 1940s, women were involved in botany, fossil collecting, archaeology, and numerous other outdoors activities. Indeed, the fact that the Girl Scouts were founded in 1912 as a way for girls to get involved in the outdoors is indicative of how normalised women in the outdoors was. Nor were the Girl Scouts the only such organisation - outdoor camps for girls existed at least as early as 1907. Safe to say, then, that women were substantially more involved in outdoors activities than common perceptions might make it seem.

However, the comment is about avid hiking, and how accessible that was. I'll admit that I don't quite know what qualifies as "avid hiking," so I can't say how common that was. However, as images like these demonstrate, there was definitely a market for camping clothes, and enough women interested in that market to sustain it. The women I've cited also likely counted as avid in their particular area, especially if they were climbing Himalayan peaks. Most importantly, however, is the particular case we're looking at. The woman the quote is referring to is Paula Jean Welden, a college student at Bennington College in Vermont in 1946. Bennington College was an all-women's school specifically tailored to drive their students to do field work. In the case of Welden, that field work involved an increasing amount of botany research, and necessitated hiking and outdoors activities. Equally, Bennington had several active outdoors clubs for women to go hiking, skiing, and swimming, and saw encouraging women to participate in these clubs as part of its raison d'etre. Even if you don't accept that hiking and camping were normal activities for women in the 1940s, it was certainly part of the university culture at Bennington.

Ultimately, though, the point is that women were very much involved in outdoors activities of all sorts, from hiking to rock climbing to surfing. This involvement exploded in the 1940s as the sports themselves grew, and as the outdoors became more and more accessible. However, it's in no way unreasonable to say that a woman could have been an avid hiker in 1946.

Sources!

This essay is specifically about rock climbing rather than hiking, but still gives a good overview of the growth of the sport and women's involvement in it.

This article is about women involved in hunting and fishing, and a particular club that started in 1940 - a bit tangential from what I wanted to talk about, but still interesting.

"Women and Nature" by Glenda Riley gives an exquisitely detailed look at women's involvement in the conservation movement, starting in the 19th century.

This essay is mostly about the sociology of men and women's perspectives on nature, but still has a good history section that talks about some sports pioneers.

I couldn't really figure out how to talk about her in the post, but Bonnie Prudden is a fantastic example of women shaping our ideas of outdoorsmanship, fitness, and exercise.