I think that the answer to your question is 'not quite'. Michelin Crossclimates are so-called all season tyres which as I understand it means that they are in effect summer tyres but with some winter capability. Probably don't need to change to full summer but I've got them as well on some nice 16" wheels.A question for you (might be a stupid question and I may be wiser after this), don’t winter tyres and Michelin cross climates do the same job? Do they not both work in snow/wet or am I missing something.
Over and above that do you then change again to summer tyres?
Apologies again if I’m being a bit thick.