I'm betting that you have a set of baloney skinned summer only tires on that bimmer?
If I'm wrong then others might be along the right track.
Summer only tires need to be over at least 40 degrees F otherwise the rubber turns into a super hard hockey puck like substance that essentially provides ZERO traction. This without even mentioning the presence of ice or snow.
That said, while snow tires might be a good idea, I suspect that just switching to an all-season compound of rubber (and upgrading to something with a little more tread depth then baloney skins) is all you need to see a HUGE difference in the situation you previously described.
Anyway, unless you live in the snow belt, Canada, New England, or the rockies, you probably don't need Snow tires but since you see temperatures which could produce snow, you definately need at minimum an all season rubber compound to address these temperatures.
Remember that your tires have an optimun temperature range rating asa well as a duty rating.
For what's it's worth sand bags and/or large chunks of steel are common and have been very helpful in every rear wheel drive vehicle I've seen or operated.
Food for thought.
-bear
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