Yeah others already answered the "why" above correctly (aggressive ackermann with cold UHP summer tires = skipping).
Getting off summer tires in the cold weather and switching to basically any tire more suited to the lower temperatures will help a lot.
Think about compliance, you want your contact patch to be flexible enough not to "skip" across the surface at low speeds. So compound-change will help a lot (like switch to all seasons) and higher sidewall should also help (changing wheels to 20 or 19). Many of us have a second set of wheels to run for the colder months, I know some people hate that, pick your poison I guess...
Or did you mean experience with all-seasons in general? Tesla has released the 21" Goodyears as all-seasons now, but I've never driven them. They should be pretty awesome though, knowing their standards...
AS tires have become very good and cater to different tastes well. If you want to bias towards performance and handling, you'd do well with a set of Michelin Pilot Sport-AS4's (they're kinda the performance benchmarkfor UHP all seasons), on the other end the CrossClimate-2's do awesome in deeper snow (and have a 3PMSF rating on an All season!) but give up driving dynamics for snow grip. They're also N/A in 21" though so that's new wheels too. Finally Conti Extreme Contact DWS06+ are supposed to be almost as good as the PS-AS4's for performance but with a bit mroe to offer in light snow. So kind of in-between the other two. I had a set of the older ones on a five series and loved them.
But any of these tires will be epically better in the cold (say under 40F) than a summer UHP!
Have fun, let us know what you go with!