We've said it before, and we'll say it again: if we had a time machine, we would never want to go back to 1940. That sexism. That racism.
But, on the other hand, they really knew how to dress to impress.
When we first see Hildy, in Walter's office, she's wearing a striking striped dress and (semi-ridiculous) hat—very stylish, very chic, and very feminine. And feminine is what she says she is; she's there with her fiancé Bruce, who, she defiantly tells her ex-husband Walter, "treats me like a woman." Her clothes show who she wants to be; a wife and a mother, with a family and a man to take care of her.
When she decides to write the story for Walter, though, she changes her clothes. Gone is the feminine attire; in its place is a plain striped jacket (which looks a lot like like the male reporter's jackets) and a utilitarian hat (which one of the reporter's teases her about). Hildy's changed from feminine, stereotypically womanly clothes to more masculine, utilitarian work clothes, symbolizing her return to the work world.
Look out world. Hildy's back.
As critic Colin Manning points out, Hildy is on a tight deadline; she needs to get the story written and catch her train to Albany and blissful domesticity. But even so, she took time to change into work clothes. She took the time to change back into the old Hildy:
"This is Hildy-the-reporter and nothing remains of Hildy-the-wife, save her purse and long feminine coat." (Source)
Maybe, like Manning says, this indicates she was chomping at the bit to get back into her work attire… and wasn't so much excited about going to Albany. Oh, and that "long feminine coat" and purse? By the time it comes to get ready to go to Albany, Hildy loses her purse and puts her coat on backwards. It's about this time that she realizes that her happy homemaker disguise is just that: a costume.
But here's another thought: maybe Hildy knows that her colleagues wouldn't take her seriously in feminine attire. The change in clothes could show the era's understanding that work and femininity were two separate worlds—and it could also illustrate how Hildy, by understanding the difference between those world, was able to operate so effectively as a career woman at a time when women were often prevented from doing so.