In reply to Katzina.W:
I've done a couple of skiing courses with Icicle. The guiding was excellent on both occasions, which, in the end is what you're really there for. The main downside is that the flats they use for valley accommodation in Chamonix are a little "basic"/"tired". To be fair, they are entirely open about this, it is reflected in their prices and you don't have to vacate them when staying in huts which is handy.
I've no experience of Jagged Globe but they would probably put you up in a 3* hotel, although they probably use the same actual guides.
Icicle are fairly specialised in The Alps and Chamonix in particular whereas Jagged Globe run stuff globally, I don't know how much difference this really makes though.
I'd be happy to use either and it may just come down to dates / availability. Whoever you use I'd be wary of parting with any cash until it's confirmed the trip will go ahead (although that's probably less of an issue with something like Mont Blanc which I think needs 2:1 guiding).