For a little fresh air on a cold day, Postman's Park is ideal. This little green space sheltered by buildings manages to pack plenty of interest in a small area. There is a tiny fishpond, some rather nice planting and, at the entrance gate, a memorial fountain and an old, blue police call box.
The main feature is, of course, the Watts Memorial to Heroic Self-Sacrifice which commemorates 'ordinary heroes'. Browse these wonderful (if tragic) Victorian stories, each so neatly encapsulated in a sentence that you don't have to linger longer than the weather allows. When you're ready to return indoors, leave by the St Martin's Le-Grand exit, cross the road, and take the escalator up to the Museum of London. One of the highlights is the (indoor) Victorian street; admission is free.
Having appreciated the atmosphere of the park, you can explore its stories further on my Postman's Park page. There are links to more detailed accounts of all the stories on the plaques.