Bill Alexander's movement-and-mime production attempts to do on stage more or less what Briggs's own animation did on video, linking up the pencilled images of the lonely-boy-befriends-iceball story with the aid of Howard Blake's pleasant, occasionally heart-touching score, which the composer has extended with an hour of extra material. But the big singing number doesn't only appear at the show's air-walking climax (a truly spectacular lift-off and a sight that's worth the ticket). The tune sneaks in at the beginning and again, twice, at the end. Already over- exposed, the melody thus loses its last ounce of specialness.
Robert North, a serious dance man and one-time director of Rambert, is wasted on the choreography, since most of the characters are swaddled in yards of thick acrylic fur. A blunt, bearish vigour is all that really comes across when the snowmen and women set to hoofing, despite an attempt to do a kind of Nutcracker in Act II with a round of national dances featuring a cowboy, Arab, Chinaman, Fred Astaire and coy ballerina resplendent in tiara and tutu. The best dance ideas go to the wildlife: a pair of hypnotised penguins, and a sleigh-team of reindeer whose cloven-hooved routine is elegant and inventive.
Dramatically, the staging adds little to the spirit of the original. The set is clumsy, trying to incorporate too much at the beginning (front door, garden, living room, stairs and bedroom all in one), and too little later on. The snowman's first-time reaction to television, electric radiators and washing-up liquid - so vivid in the book - get lost in the general galumphing about. Only the episode of basking in the chest- freezer (used deftly here as an opportunity to attach flying wires) exploits its full potential as theatre. Which is not to say that young children won't love this show. When the boy (appealingly played by young Drew McOnie) wakes up next day to find his crystallised friend reduced to a puddle on the lawn, my seven-year-old daughter flung herself across my seat and sobbed.
A more even-handed treat is to be had in The Secret Garden at the Little Angel Theatre, tucked away down its own secret alleyway in Islington. Intimate, low-key and low-tech, the resident company's marionette version of Frances Hodgson Burnett's Edwardian novel leaves children shiny-eyed with wonder and adults with a lump in the throat the size of a wheelbarrow. This is all the more remarkable since the suspension of disbelief depends on the audience learning to ignore the five black-swathed puppeteers who manipulate the jointed wooden figures, and whose delicate operations sometimes interpose them between the audience and the action.
Control of scale is the chief delight of this production. Mostly, the puppets are 18 inches tall. But for the scenes at Mistlethwaite Manor, the lens suddenly pulls wide to show an intricate cross-section of the whole interior, built to scale like an Edwardian doll's house. The characters then shrink to tiny, rigid rod puppets, whose rattling perambulations up and down the flights of stairs add an unexpected shot of comedy.
Attention to detail is masterly throughout: the picture that slips on the wall every time petulant Mary stamps her foot; the almost imperceptible brightening of the puppets' facial expressions as the plot progresses; Mary's redemptive discovery of green shoots under the dead leaves of winter. The denouement in the garden when the flowers are in bloom and crippled Colin learns to walk is so exquisitely done that you scarcely dare breathe lest it be blown away. It doesn't matter how close you sit: there are no tricks or illusions here. Adaptor Karen Prell (of the Henson Organisation) and director Christopher Leith have created a miniature masterpiece of theatre art. Find a child to take if you must, but go.
Snowman: Peacock, WC2 (0171 863 8222), to 30 January. Secret Garden: Little Angel, N1 (0171 226 1787), in rep to 31 January.