An Xdrive will cope in anything but the most extreme conditions on summer tyres with out to much stress, however remember it's not just about getting going steering and stopping are useful things to be able to do as well. That said my X5 with fat summer tyres has many times pulled the horse trailer with a couple of fat horses on board out of slippery wet grass fields and coped with snotty gateways where others have had to wait for a tractor to assist.
Winter Tyres use a different compound that only really starts to work below about 12 C so on a cold frosty morning they are not compromised. While a summer tyre still works it's stopping distance will be increased. With the AMG's on a cold morning on a moist road any acceleration would give the traction control a work out, while on winters it wouldn't be noticed.
Just remember just because they grip better in poor conditions they don't increase our driving skill to that of a World Rally driver !!