It's a bit late, but this is what we did in the winter holidays:
Visited Kew Gardens in the fog. http://www.kew.org/ We have a season ticket, so it doesn't matter if we don't see a lot of the gardens. It was amazing - very atmospheric. We went into the Snow Dome, which sprayed foam everywhere to simulate a snow storm (that's often the closest we get in London) and in the indoor play centre Climbers and Creepers, which was a lot of fun, even for the bigger children. http://www.kew.org/education/cc.html Check out the giant millipedes!
Walked with my husband in Golders Hill Park where I discovered the Hill Garden and pergola for the first time, even though I have been visiting the park since I was a small child and we have lived within walking distance for nearly 5 years! http://www.cityoflondon.gov.uk/NR/rdonlyres/E52681A0-40B6-41E1-9940-4B467B06ACFA/0/OS_HH_trailsleaflet.pdf. It was so good that I went back the following week with our toddler, who was fascinated to see some birds having a bath in the pond.
Had a family outing to the South Bank, to see the Globe Theatre http://www.shakespeares-globe.org/ which was really interesting. We strolled over to the Tate Modern to eat lunch on the benches outside and see this year's Unilever installation Shibboleth http://www.tate.org.uk/modern/exhibitions/dorissalcedo/default.shtm We reckoned that it was worth looking at if you are nearby, but not worth going specially, unlike last year, when we had a thrilling time on the slides. http://www.tate.org.uk/modern/exhibitions/carstenholler/default.shtm
Last cultural outing - to the First Emperor exhibition at the British Museum, which was amazing, although not so good for younger children. http://www.britishmuseum.org/whats_on/all_current_exhibitions/the_first_emperor.aspx It has been so popular that they are opening late in the evening to accommodate all the people who would like to see some of the Terracotta Army.
I stayed up late on New Year's Eve to watch the fireworks out of the loft window. Yes they are a terrible waste of money and inconsiderate as well, but since they are there, I might as well enjoy them!