It might surprise some to know it snows in California; but, it does and it does so quite heavily. I have a beetle and my observations are that is is a moderately heavy car for its small looks, and is a front wheel drive. there is nothing special, good or bad, about it in the winter.
The only problem is that there isn't a whole lot of fender clearance. This makes it hard to put chains on and limits your selection in tire chains (tire chains are not legal, or common, in a lot of places; so, this may not apply to you). The fender-wells tend to pack up with snow pretty quickly too. However, none of these problems are unique to the beetle.