I'm not really wanting to buy winter tires just for a 1 week vacation to visit my family. I'm thinking I'll get some chains and give that a go. I spent 10 years driving in ice and snow there, but always had 4x4. Come to think of it though, I rarely used 4x4. My best snow vehicle was a 88 Bronco that I was told had a "posi". Wish I knew exactly what it had. I'm assuming that it was a limited slip and not a locker. I had a terrible time with my 2011 F150 4x4 limited slip last year, but I'm assuming that was due to the 35 inch Mickey Thompson mud tires. I couldn't go anywhere in 2wd and in 4x4 it wasn't much better.
First: Tires are
the only contract that your car has with the ground. If you have conditions where you can put on chains that's different.
Traction depends also on the weight you have on your serving axle. Best for this is a 911 or beetle, worst is a pickup. But in most cases you also need to stop the car quickly too. 4x4, limited slip does not help to stop a car in any case. If your travelling in lonely areas it might be not that issue but in cities it is for sure.
Winter tires get their grip through 2 things: They are much softer in cold conditions and their profile keeps snow and snow crystals inside. frozen water (due to the pressure of the vehicle weight) gets suck to the snow inside the profile.
you don't have this effect on other tires.
I got on bmw z coupe with Sommer tires at the moment and my traction is damm bad as we have less than 10 degrees celsius outside, on dry conditions. really noticeable. the work best with 25 degrees.
On my former Iveco I had Michelin xzl. these are told as the best tires for sand and mud but at 0 degrees C these tires went extremely slippery, even on dry conditions.
btw: a second set of tires is not that expensive because you save the summer tires in the meantime.
But anyway do what ever works best for you. I live in a city with a million people and in a country without speed limit (partly ;-) ).