That would be Kate Winslet as Marianne in the 1995 movie version. She has hiked to the top of a hill to see Combe Magna, Willoughby's house, and to recite from Shakespeare's sonnet 116, which you can read (along with my commentary) in this National Poetry Month post from 2009 if you're so inclined. Of course, Combe Magna is thirty miles away from Cleveland Park, so Marianne couldn't actually have hiked there. Nor is there any mention of Marianne reciting sonnets, although it certainly does seem like something she might do.
What also does not happen in this chapter:
I'm referring to what happens between about 3:30 and 6:40 in particular - the part prior to that includes last chapter's painful meeting between Elinor and Edward. The part after that continues into what is actually next chapter. My point is, there's nothing particularly dramatic in the text about how Marianne gets her cold. But Emma Thompson made it memorably dramatic in the 1995 movie version (sorry I couldn't find film footage of Alan Rickman staggering in the door with a sodden Marianne and collapsing to his knees - SO swoon-worthy). She has Brandon go out into the rain and carry a drenched Marianne home, effectively reprising Willoughby's "rescue" of Marianne from earlier in the book. Only this time, Marianne is well and truly helpless and her rescuer sets out on purpose after her, instead of stumbling (almost literally) across her. Andrew Davies knows a good thing when he sees it, so he nabbed Thompson's idea and sends Brandon of on a white horse to find Marianne. And then he has Brandon nearly strip her when he gets her home. Because everyone knows Austen needs sexing up - or at least that's Davies's apparent belief, and he is fond of making his heroes wet.
What DOES happen in this chapter:
Elinor and Marianne head to Cleveland Park, home of the Palmers, along with Mrs Jennings. Colonel Brandon and Mr Palmer follow behind. Brandon tells Elinor that he's visited the parsonage at Delaford, and he explains the repairs and improvements he intends to make for Edward's benefit. Mrs Jennings continues to believe that Brandon has a thing for Elinor. Elinor realizes it seems as if Brandon might have a thing for her, since he treats her as a confidante and they converse easily, but she notices that he watches Marianne carefully and shows extreme concern over her health when she comes down with a head cold.
The Dashwoods plan to stay there for a week or so, then return to Barton Cottage. We'll see what happens now that Marianne is ill.