This is a little conditions report based on a quick trip I made on the two sides. Originally I had intended to go all the way to the Leschaux, but so-so visibility and complicated glacial condition made me do an about face before the Trelaporte bend. Here's it, however (a version of this was posted also on UkClimbing.Com):
French side: there's decent snow from 1000m to around 3200m, and it's bloody FREEZING (-10° in Cham and -15° at Montenvers). However, above more or less 3300 m the snow cover drops quite dramatically in several areas - the Argentiere basin expecially. Having not made it beyond the Trelaporte bend I don't have first hand evidence of the Talefre/Jorasses beyond quick glimpses (looked plastered with ice, but grey-ish). On the frontier ridge and on MB there is a lot of wind, and generally speaking conditions there appears to be surprisingly "wintery" - just without plenty of snow. On the other hand, there was a lot of verglas everywhere (the Drus looked spectacular).
Italian side: more or less the same, but with less snow even at lower altitudes. This is anyway bound to change in a couple of days - the forecast give some snowfall on this side and the watershed for the weekend. Temperatures here are again extremely cold, and again there are strong western / north western winds above a certain altitude
On practical terms, I had no time to stop at the OHM, but in Courmayeur the info are as follows - Gabarrou/Albinoni and Lafaille and the Triangle are in good conditions and regularly done, Hidden Couloir and Supercouloir are ok; the Modica's conditions are bad, the rest of the Tacul area is "dubious" - however all rimaye are open and difficult . Almost everything on the Argentiere "bottom" (Petit Viking etc.) and the Aig. Carreè area is in conditions, but access there is made more difficult by the closure of the last section of the Montets telepherique (and again, rimaye are in bad state). There's also a lot that can be done on the Talefre and the Petit Jorasses, but I've some indication that (again!) the access from the huts to the wall are quite difficult.
The very high mountain (MB, Jorasses, Verte) is threatened by wind, very low temperatures and general winter conditions (in other words, right now more or less off limits).
On a personal note, the Plan-Midi routes (Couloir Mallory, etc.) seems to be in rather decent state.