If you already have a winter beater, leave it alone, do not sell it for a set of winter wheels and tires. Having a winter beater is the better option.
That said, my winter beater is a 400-hp Cadillac CTS-V and my wife's is a 306-hp Nissan 350Z; both have winter tires. No problem with driving in the snow. Both of us have been driving RWD vehicles in winter for more than 10 years. Previously, I drove a 2WD ECSB GMT800 on all-terrain and my wife a BMW E36 M3 on various winter tires.