Its normal on the 370's in colder wweather - particularly if you are using the Brigestones that have relatively hard sidewalls.
Unless it is still doing it when the tyres have warmed up, then it needs checking.
When turning the car on full lock from cold will make it feel as thow the tyres are slipping sideways across the surface (like a judder). To do with the geometry at the front of the 370's that is different from the 350's. When I first got my 370 (after two 350's) I was a bit taken aback but you soon forget about and if you change to softer sidewall tyres (as I have done) it all but elimates it. .